public static double EnergyBalanceNormAtInterface(XDGField P, VectorField <XDGField> U, ConventionalDGField[] Umean, SinglePhaseField C, double muA, double muB, double sigma, int momentFittingOrder)
{
LevelSetTracker LsTrk = P.Basis.Tracker;
double energyBal_Norm = 0.0;
ScalarFunctionEx energyBalFunc = GetEnergyBalanceFunc(P, U, Umean, C, muA, muB, sigma, true);
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, momentFittingOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, momentFittingOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
energyBalFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
energyBal_Norm += ResultsOfIntegration[i, 0];
}
}
).Execute();
return(energyBal_Norm.Sqrt());
}
public static double CurvatureEnergy(LevelSetTracker LsTrk, SinglePhaseField Curvature, double sigma, ConventionalDGField[] uI, bool ExtVel, bool Norm, int momentFittingorder)
{
double EnergyCurv = 0.0;
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, momentFittingorder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
ScalarFunctionEx CurvEnergyFunc = GetCurvatureEnergyFunc(LsTrk, Curvature, sigma, uI, ExtVel, Norm);
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, momentFittingorder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
CurvEnergyFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
EnergyCurv += ResultsOfIntegration[i, 0];
}
}
).Execute();
if (Norm)
{
EnergyCurv.Sqrt();
}
return(EnergyCurv);
}
public static double EnergyJumpAtInterface(LevelSetTracker LsTrk, VectorField <XDGField> Velocity, XDGField Pressure, double muA, double muB, bool Norm, int momentFittingorder)
{
double EnergyJump = 0.0;
ScalarFunctionEx EnergyJumpFunc = GetEnergyJumpFunc(LsTrk, Velocity, Pressure, muA, muB, Norm);
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, momentFittingorder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, momentFittingorder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EnergyJumpFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
EnergyJump += ResultsOfIntegration[i, 0];
}
}
).Execute();
if (Norm)
{
EnergyJump.Sqrt();
}
return(EnergyJump);
}
public static double SurfaceEnergyChangerate(LevelSetTracker LsTrk, ConventionalDGField[] uI, double sigma, bool Norm, int momentFittingorder)
{
double Changerate_Surface = 0.0;
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, momentFittingorder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
ScalarFunctionEx SurfaceChangerate = GetInterfaceDivergenceFunc(LsTrk, uI, Norm);
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, momentFittingorder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
SurfaceChangerate(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
Changerate_Surface += ResultsOfIntegration[i, 0];
}
}
).Execute();
double Changerate_Esurf;
if (Norm)
{
Changerate_Esurf = sigma * Changerate_Surface.Sqrt();
}
else
{
Changerate_Esurf = sigma * Changerate_Surface;
}
return(Changerate_Esurf);
}
/// <summary>
/// Change-of-basis, in cell 0
/// </summary>
/// <param name="jCell"></param>
/// <param name="pl"></param>
public MultidimensionalArray GetChangeofBasisMatrix(int jCell, PolynomialList pl)
{
var m_Context = this.GridDat;
int N = this.Length;
int M = pl.Count;
int J = this.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (jCell < 0 || jCell >= J)
{
throw new ArgumentOutOfRangeException("cell index out of range");
}
MultidimensionalArray Mtx = MultidimensionalArray.Create(N, M);
var cellMask = new CellMask(m_Context, new[] { new Chunk()
{
i0 = jCell, Len = 1
} }, MaskType.Geometrical);
// we project the basis function from 'jCell1' onto 'jCell0'
CellQuadrature.GetQuadrature(new int[2] {
N, M
}, m_Context,
(new CellQuadratureScheme(true, cellMask)).Compile(m_Context, this.Degree + pl.MaxAbsoluteDegree), // integrate over target cell
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray _EvalResult) {
NodeSet nodes_Cell0 = QR.Nodes;
Debug.Assert(Length == 1);
//NodesGlobal.Allocate(1, nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
//m_Context.TransformLocal2Global(nodes_Cell0, jCell0, 1, NodesGlobal, 0);
//var nodes_Cell1 = new NodeSet(GridDat.iGeomCells.GetRefElement(jCell1), nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
//m_Context.TransformGlobal2Local(NodesGlobal.ExtractSubArrayShallow(0, -1, -1), nodes_Cell1, jCell1, null);
//nodes_Cell1.LockForever();
var phi_0 = this.CellEval(nodes_Cell0, jCell, 1).ExtractSubArrayShallow(0, -1, -1);
MultidimensionalArray R = MultidimensionalArray.Create(QR.NoOfNodes, pl.Count);
pl.Evaluate(nodes_Cell0, R);
var EvalResult = _EvalResult.ExtractSubArrayShallow(0, -1, -1, -1);
EvalResult.Multiply(1.0, R, phi_0, 0.0, "knm", "km", "kn");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
Debug.Assert(Length == 1);
var res = ResultsOfIntegration.ExtractSubArrayShallow(0, -1, -1);
Mtx.Clear();
Mtx.Acc(1.0, res);
}).Execute();
return(Mtx);
}
/// <summary>
/// Computes the Integral of a given function over the zero iso-contour of the Level-Set
/// </summary>
/// <param name="LsTrk">Level-Set tracker</param>
/// <param name="func">function which is integrated</param>
/// <param name="HMForder"></param>
/// <param name="spc">species, over whose surface is integrated</param>
/// <returns>Integral of <param name="func">func</param> over all MPI processors</returns>
static public double GetIntegralOverZeroLevelSet(LevelSetTracker LsTrk, ScalarFunctionEx func, int HMForder, SpeciesId spc)
{
using (new FuncTrace()) {
if (LsTrk.LevelSets.Count != 1)
{
throw new NotImplementedException();
}
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new SpeciesId[] { spc }, HMForder, 1).XQuadSchemeHelper;
// new XQuadSchemeHelper(LsTrk, momentFittingVariant);
// Classic HMF uses order+1 for Surface Integrals and additionally 1 order higher for the HMF system
// e.g order-2 is the cached quad rule
if (SchemeHelper.MomentFittingVariant == XQuadFactoryHelper.MomentFittingVariants.Classic)
{
HMForder -= 2;
}
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
double force = 0;
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
func(i0, Length, QR.Nodes, EvalResult);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
force += ResultsOfIntegration[i, 0];
}
}
).Execute();
double localForce = force;
double globalForce;
unsafe
{
csMPI.Raw.Allreduce(
(IntPtr)(&localForce),
(IntPtr)(&globalForce),
1,
csMPI.Raw._DATATYPE.DOUBLE,
csMPI.Raw._OP.SUM,
csMPI.Raw._COMM.WORLD);
}
return(globalForce);
}
}
/// <summary>
/// Calculate Forces acting from fluid onto the particle
/// </summary>
internal double[] Forces(out List <double[]>[] stressToPrintOut, CellMask cutCells)
{
double[] tempForces = new double[m_SpatialDim];
double[] IntegrationForces = tempForces.CloneAs();
List <double[]>[] stressToPrint = new List <double[]> [m_SpatialDim];
stressToPrint[0] = new List <double[]>();
stressToPrint[1] = new List <double[]>();
for (int d = 0; d < m_SpatialDim; d++)
{
void ErrFunc(int CurrentCellID, int Length, NodeSet Ns, MultidimensionalArray result)
{
int K = result.GetLength(1);
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Length, K, m_SpatialDim, m_SpatialDim);
MultidimensionalArray pARes = MultidimensionalArray.Create(Length, K);
MultidimensionalArray Normals = m_LevelSetTracker.DataHistories[0].Current.GetLevelSetNormals(Ns, CurrentCellID, Length);
for (int i = 0; i < m_SpatialDim; i++)
{
m_U[i].EvaluateGradient(CurrentCellID, Length, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
m_P.Evaluate(CurrentCellID, Length, Ns, pARes);
for (int j = 0; j < Length; j++)
{
for (int k = 0; k < K; k++)
{
result[j, k] = StressTensor(Grad_UARes, pARes, Normals, m_FluidViscosity, k, j, m_SpatialDim, d);
double t = Math.PI * (1 - Math.Sign(Normals[j, k, 1])) / 2 + Math.Acos(Normals[j, k, 0]);
stressToPrint[d].Add(new double[] { t, result[j, k] });
}
}
}
int[] noOfIntegrals = new int[] { 1 };
XQuadSchemeHelper SchemeHelper = m_LevelSetTracker.GetXDGSpaceMetrics(new[] { m_LevelSetTracker.GetSpeciesId("A") }, m_RequiredOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, cutCells);
ICompositeQuadRule <QuadRule> surfaceRule = cqs.Compile(m_LevelSetTracker.GridDat, m_RequiredOrder);
CellQuadrature.GetQuadrature(noOfIntegrals, m_GridData, surfaceRule,
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) { ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0)); },
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { IntegrationForces[d] = ForceTorqueSummationWithNeumaierArray(IntegrationForces[d], ResultsOfIntegration, Length); }
).Execute();
}
stressToPrintOut = stressToPrint.CloneAs();
return(tempForces = IntegrationForces.CloneAs());
}
void OrthonormalityTest()
{
Basis B = f1.Basis;
int N = B.Length;
var Mtx = new FullMatrix(N, N);
double TotErrSum = 0.0;
CellQuadrature.GetQuadrature(new int[] { N, N }, this.GridDat,
(new CellQuadratureScheme(true)).Compile(GridDat, Math.Min(B.Degree * 2, 16)),
delegate(MultidimensionalArray NodesUntransformed, int iKref) {
var ret = new NodeSetController.NodeSetContainer[] {
GridDat.NSC.CreateContainer(NodesUntransformed, iKref)
};
return(ret);
},
delegate(int i0, int Length, int NoOfNodes, MultidimensionalArray EvalResult) { // void Del_Evaluate
var BasisVal = B.CellEval(0, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
for (int i = 0; i < Length; i++)
{
var MassMtx = ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1);
double errsum = 0;
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
double soll = (n == m) ? 1.0 : 0.0;
errsum += Math.Abs(MassMtx[m, n] - soll);
}
}
TotErrSum += errsum;
}
}).Execute();
Console.WriteLine("orthonormality error sum:" + TotErrSum);
}
public static double GetKineticDissipation(LevelSetTracker LsTrk, DGField[] Velocity, double[] mu, int momentFittingOrder, int HistInd = 1)
{
using (new FuncTrace()) {
int D = LsTrk.GridDat.SpatialDimension;
if (Velocity.Count() != D)
{
throw new ArgumentException();
}
if (LsTrk.SpeciesIdS.Count != mu.Length)
{
throw new ArgumentException();
}
double dE = 0.0;
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(LsTrk.SpeciesIdS.ToArray(), momentFittingOrder, HistInd).XQuadSchemeHelper;
for (int iSpc = 0; iSpc < LsTrk.SpeciesIdS.Count; iSpc++)
{
SpeciesId spcId = LsTrk.SpeciesIdS[iSpc];
double _mu = mu[iSpc];
var Uspc = Velocity.Select(u => (u as XDGField).GetSpeciesShadowField(spcId)).ToArray();
ScalarFunctionEx changerate_dEspc = GetSpeciesKineticDissipationFunc(Uspc, _mu);
CellQuadratureScheme vqs = SchemeHelper.GetVolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
vqs.Compile(LsTrk.GridDat, momentFittingOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
changerate_dEspc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
dE += ResultsOfIntegration[i, 0];
}
}
).Execute();
}
return(dE);
}
}
/// <summary>
/// Computes the energy stored in the fluid interface of a two-phase flow.
/// </summary>
/// <param name="LsTrk"></param>
/// <param name="sigma"></param>
public static double GetSurfaceEnergy(LevelSetTracker LsTrk, double sigma)
{
using (new FuncTrace()) {
if (LsTrk.LevelSets.Count != 1)
{
throw new NotImplementedException();
}
double totSurface = 0;
int order = 0;
if (LsTrk.GetCachedOrders().Count > 0)
{
order = LsTrk.GetCachedOrders().Max();
}
else
{
order = 1;
}
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, order, 1).XQuadSchemeHelper;
//var SchemeHelper = new XQuadSchemeHelper(LsTrk, momentFittingVariant, LsTrk.GetSpeciesId("A"));
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, order),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
totSurface += ResultsOfIntegration[i, 0];
}
}
).Execute();
return(totSurface * sigma);
}
}
/// <summary>
/// Calculate Forces acting from fluid onto the particle
/// </summary>
internal double Torque(double[] position, CellMask cutCells)
{
double tempTorque = new double();
void ErrFunc2(int j0, int Len, NodeSet Ns, MultidimensionalArray result)
{
int K = result.GetLength(1);
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, m_SpatialDim, m_SpatialDim);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray Normals = m_LevelSetTracker.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < m_SpatialDim; i++)
{
m_U[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
m_P.Evaluate(j0, Len, Ns, pARes);
for (int j = 0; j < Len; j++)
{
MultidimensionalArray Ns_Global = Ns.CloneAs();
m_LevelSetTracker.GridDat.TransformLocal2Global(Ns, Ns_Global, j0 + j);
for (int k = 0; k < K; k++)
{
result[j, k] = TorqueStressTensor(Grad_UARes, pARes, Normals, Ns_Global, m_FluidViscosity, k, j, position);
}
}
}
var SchemeHelper2 = m_LevelSetTracker.GetXDGSpaceMetrics(new[] { m_LevelSetTracker.GetSpeciesId("A") }, m_RequiredOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs2 = SchemeHelper2.GetLevelSetquadScheme(0, cutCells);
CellQuadrature.GetQuadrature(new int[] { 1 }, m_LevelSetTracker.GridDat, cqs2.Compile(m_LevelSetTracker.GridDat, m_RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc2(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
tempTorque = ForceTorqueSummationWithNeumaierArray(tempTorque, ResultsOfIntegration, Length);
}
).Execute();
return(tempTorque);
}
public static void ProjectEnergyBalanceNorm(this SinglePhaseField err, double alpha, XDGField P, VectorField <XDGField> U, ConventionalDGField[] Umean, SinglePhaseField C,
double muA, double muB, double sigma, int momentFittingOrder)
{
var LsTrk = U[0].Basis.Tracker;
int D = LsTrk.GridDat.SpatialDimension;
ScalarFunctionEx ErrFunc = GetEnergyBalanceFunc(P, U, Umean, C, muA, muB, sigma, true);
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, momentFittingOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, momentFittingOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
err.SetMeanValue(i0 + i, ResultsOfIntegration[i, 0].Sqrt());
}
}
).Execute();
}
public static double GetInterfaceShearViscosityEnergyCR(LevelSetTracker LsTrk, ConventionalDGField[] uI, double muI, int momentFittingOrder)
{
double shearViscEnergy = 0.0;
ScalarFunctionEx shearViscEnergyFunc = GetInterfaceShearViscosityEnergyCRFunc(LsTrk, uI, false);
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, momentFittingOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, momentFittingOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
shearViscEnergyFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
shearViscEnergy += ResultsOfIntegration[i, 0];
}
}
).Execute();
return(muI * shearViscEnergy);
}
void SpecialProjection(LevelSetTracker LsTrk, int order, DGField[] Uin, VectorField <SinglePhaseField> Uout)
{
var CC = LsTrk.Regions.GetCutCellMask();
var gDat = LsTrk.GridDat;
// get quadrature rules
// ====================
//XQuadSchemeHelper H = new XQuadSchemeHelper(LsTrk, MomentFittingVariant);
var H = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, order, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = H.GetLevelSetquadScheme(0, CC);
ICompositeQuadRule <QuadRule> surfRule = cqs.Compile(gDat, order);
ICompositeQuadRule <CellBoundaryQuadRule> bndyRule = (new CellBoundaryQuadratureScheme(true, CC)).Compile(gDat, order);
// Compute Mass matrix and RHS for the 'strange' projection
// ========================================================
int L = CC.NoOfItemsLocally;
var Q = new QuadratureKernels(Uin, L);
Q.BlockCnt = 0;
CellQuadrature.GetQuadrature(
new int[] { Q.Nnx + Q.D, Q.Nnx },
gDat,
surfRule,
Q.Evaluate, Q.SaveIntegrationResults_surf).Execute();
Debug.Assert(Q.BlockCnt == L);
Q.BlockCnt = 0;
CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(
new int[] { Q.Nnx + Q.D, Q.Nnx },
gDat,
bndyRule,
Q.Evaluate, Q.SaveIntegrationResults_bndy).Execute();
Debug.Assert(Q.BlockCnt == L);
// solve the non-diagonal mass matrix systems
// ==========================================
int BlkCnt = 0;
foreach (int jCell in CC.ItemEnum)
{
var MassMatrix = Q.MassMatrix.ExtractSubArrayShallow(BlkCnt, -1, -1);
var RHS = Q.RHS.ExtractSubArrayShallow(BlkCnt, -1, -1);
// Die "Massenmatrix" muss nicht unbedingt invbar sein, daher: Least-Squares solve
MassMatrix.LeastSquareSolve(RHS);
for (int d = 0; d < Q.D; d++)
{
for (int n = 0; n < Q.Nnx; n++)
{
Uout[d].Coordinates[jCell, n] = RHS[n, d];
}
}
BlkCnt++;
}
}
/// <summary>
/// Calculates the Torque around the center of mass
/// </summary>
/// <param name="U"></param>
/// <param name="P"></param>
/// <param name="momentFittingVariant"></param>
/// <param name="muA"></param>
/// <param name="particleRadius"></param>
/// <returns></returns>
static public void GetCellValues(VectorField <XDGField> U, XDGField P,
double muA, double particleRadius, SinglePhaseField P_atIB, SinglePhaseField gradU_atIB, SinglePhaseField gradUT_atIB)
{
var LsTrk = U[0].Basis.Tracker;
int D = LsTrk.GridDat.SpatialDimension;
var UA = U.Select(u => u.GetSpeciesShadowField("A")).ToArray();
if (D > 2)
{
throw new NotImplementedException("Currently only 2D cases supported");
}
int RequiredOrder = U[0].Basis.Degree * 3 + 2;
//if (RequiredOrder > agg.HMForder)
// throw new ArgumentException();
Console.WriteLine("Cell values calculated by: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
ConventionalDGField pA = null;
double circumference = new double();
pA = P.GetSpeciesShadowField("A");
for (int n = 0; n < 4; n++)
{
ScalarFunctionEx ErrFunc_CellVal = delegate(int j0, int Len, NodeSet Ns, MultidimensionalArray result) {
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, D, D);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
// Evaluate tangential velocity to level-set surface
var Normals = LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < D; i++)
{
UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1));
}
pA.Evaluate(j0, Len, Ns, pARes);
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
double acc2 = 0.0;
switch (n)
{
case 0: // Pressure part
acc += pARes[j, k] * Normals[j, k, 0];
acc *= -Normals[j, k, 1] * particleRadius;
acc2 += pARes[j, k] * Normals[j, k, 1];
acc2 *= Normals[j, k, 0] * particleRadius;
result[j, k] = acc + acc2;
break;
case 1: // GradU part
acc -= (1 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0]; // Attention was 2 times
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc *= -Normals[j, k, 1] * particleRadius;
acc2 -= (1 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc2 -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc2 *= Normals[j, k, 0] * particleRadius;
result[j, k] = acc + acc2;
break;
case 2: // GradU_T part
acc -= (1 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0]; // Attention was 2 times
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
acc *= -Normals[j, k, 1] * particleRadius;
acc2 -= (1 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1]; // Attention was 2 times
acc2 -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
acc2 *= Normals[j, k, 0] * particleRadius;
result[j, k] = acc + acc2;
break;
case 3: // Standardization with radians
result[j, k] = 1;
break;
default:
throw new NotImplementedException();
}
}
}
};
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper; // new XQuadSchemeHelper(LsTrk, momentFittingVariant, );
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc_CellVal(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
switch (n)
{
case 0:
P_atIB.SetMeanValue(i0, ResultsOfIntegration[i, 0]);
break;
case 1:
gradU_atIB.SetMeanValue(i0, ResultsOfIntegration[i, 0]);
break;
case 2:
gradUT_atIB.SetMeanValue(i0, ResultsOfIntegration[i, 0]);
break;
case 3:
circumference += ResultsOfIntegration[i, 0];
P_atIB.SetMeanValue(i0, P_atIB.GetMeanValue(i0) / ResultsOfIntegration[i, 0]);
gradU_atIB.SetMeanValue(i0, gradU_atIB.GetMeanValue(i0) / ResultsOfIntegration[i, 0]);
gradUT_atIB.SetMeanValue(i0, gradUT_atIB.GetMeanValue(i0) / ResultsOfIntegration[i, 0]);
break;
default:
throw new NotImplementedException();
}
}
}
).Execute();
}
Console.WriteLine("Circle circumference: " + circumference);
}
/// <summary>
/// Update forces and torque acting from fluid onto the particle
/// </summary>
/// <param name="U"></param>
/// <param name="P"></param>
/// <param name="LsTrk"></param>
/// <param name="muA"></param>
public void UpdateForcesAndTorque(VectorField <SinglePhaseField> U, SinglePhaseField P,
LevelSetTracker LsTrk,
double muA)
{
if (skipForceIntegration)
{
skipForceIntegration = false;
return;
}
int D = LsTrk.GridDat.SpatialDimension;
// var UA = U.Select(u => u.GetSpeciesShadowField("A")).ToArray();
var UA = U.ToArray();
int RequiredOrder = U[0].Basis.Degree * 3 + 2;
//int RequiredOrder = LsTrk.GetXQuadFactoryHelper(momentFittingVariant).GetCachedSurfaceOrders(0).Max();
//Console.WriteLine("Order reduction: {0} -> {1}", _RequiredOrder, RequiredOrder);
//if (RequiredOrder > agg.HMForder)
// throw new ArgumentException();
Console.WriteLine("Forces coeff: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
ConventionalDGField pA = null;
//pA = P.GetSpeciesShadowField("A");
pA = P;
#region Force
double[] forces = new double[D];
for (int d = 0; d < D; d++)
{
ScalarFunctionEx ErrFunc = delegate(int j0, int Len, NodeSet Ns, MultidimensionalArray result) {
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, D, D);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
// Evaluate tangential velocity to level-set surface
var Normals = LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < D; i++)
{
UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
pA.Evaluate(j0, Len, Ns, pARes);
if (LsTrk.GridDat.SpatialDimension == 2)
{
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
// pressure
switch (d)
{
case 0:
acc += (pARes[j, k]) * Normals[j, k, 0];
acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
break;
case 1:
acc += (pARes[j, k]) * Normals[j, k, 1];
acc -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
break;
default:
throw new NotImplementedException();
}
result[j, k] = acc;
}
}
}
else
{
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
// pressure
switch (d)
{
case 0:
acc += pARes[j, k] * Normals[j, k, 0];
acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 2] * Normals[j, k, 2];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 2, 0] * Normals[j, k, 2];
break;
case 1:
acc += pARes[j, k] * Normals[j, k, 1];
acc -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 2] * Normals[j, k, 2];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 2, 1] * Normals[j, k, 2];
break;
case 2:
acc += pARes[j, k] * Normals[j, k, 2];
acc -= (2 * muA) * Grad_UARes[j, k, 2, 2] * Normals[j, k, 2];
acc -= (muA) * Grad_UARes[j, k, 2, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 2, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 0, 2] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 1, 2] * Normals[j, k, 1];
break;
default:
throw new NotImplementedException();
}
result[j, k] = acc;
}
}
}
};
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
//var SchemeHelper = new XQuadSchemeHelper(LsTrk, momentFittingVariant, );
//CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, this.cutCells_P(LsTrk));
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, RequiredOrder), // agg.HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
forces[d] += ResultsOfIntegration[i, 0];
}
}
).Execute();
}
#endregion
#region Torque
double torque = 0;
ScalarFunctionEx ErrFunc2 = delegate(int j0, int Len, NodeSet Ns, MultidimensionalArray result) {
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, D, D);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
// Evaluate tangential velocity to level-set surface
var Normals = LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < D; i++)
{
UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
//var trafo = LsTrk.GridDat.Edges.Edge2CellTrafos;
//var trafoIdx = LsTrk.GridDat.TransformLocal2Global(Ns)
//var transFormed = trafo[trafoIdx].Transform(Nodes);
//var newVertices = transFormed.CloneAs();
//GridData.TransformLocal2Global(transFormed, newVertices, jCell);
MultidimensionalArray tempArray = Ns.CloneAs();
LsTrk.GridDat.TransformLocal2Global(Ns, tempArray, j0);
pA.Evaluate(j0, Len, Ns, pARes);
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
double acc2 = 0.0;
// Calculate the torque around a circular particle with a given radius (Paper Wan and Turek 2005)
acc += (pARes[j, k] * Normals[j, k, 0]);
acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
//acc *= -Normals[j, k, 1] * this.radius_P;
acc *= -Normals[j, k, 1] * (this.currentPos_P[0][1] - tempArray[k, 1]).Abs();
acc2 += pARes[j, k] * Normals[j, k, 1];
acc2 -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc2 -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc2 -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
//acc2 *= Normals[j, k, 0] * this.radius_P;
acc2 *= Normals[j, k, 0] * (this.currentPos_P[0][0] - tempArray[k, 0]).Abs();
result[j, k] = acc + acc2;
}
}
};
var SchemeHelper2 = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
//var SchemeHelper = new XQuadSchemeHelper(LsTrk, momentFittingVariant, );
//CellQuadratureScheme cqs2 = SchemeHelper2.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadratureScheme cqs2 = SchemeHelper2.GetLevelSetquadScheme(0, this.cutCells_P(LsTrk));
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs2.Compile(LsTrk.GridDat, RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc2(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
torque += ResultsOfIntegration[i, 0];
}
}
).Execute();
double underrelaxationFT = 1.0;
double[] temp_underR = new double[D + 1];
for (int k = 0; k < D + 1; k++)
{
temp_underR[k] = underrelaxation_factor;
}
if (iteration_counter_P == 0)
{
underrelaxationFT = 1;
}
else if (underrelaxationFT_constant == true)
{
underrelaxationFT = underrelaxation_factor * Math.Pow(10, underrelaxationFT_exponent);
}
else if (underrelaxationFT_constant == false)
{
//double[] temp_underR = new double[D + 1];
bool underrelaxation_ok = false;
underrelaxationFT_exponent = 1;
for (int j = 0; j < D; j++)
{
underrelaxation_ok = false;
temp_underR[j] = underrelaxation_factor;
for (int i = 0; underrelaxation_ok == false; i++)
{
if (Math.Abs(temp_underR[j] * forces[j]) > Math.Abs(forces_P[0][j]))
{
underrelaxationFT_exponent -= 1;
temp_underR[j] = underrelaxation_factor * Math.Pow(10, underrelaxationFT_exponent);
}
else
{
underrelaxation_ok = true;
if (underrelaxationFT_exponent > -0)
{
underrelaxationFT_exponent = -0;
temp_underR[j] = underrelaxation_factor * Math.Pow(10, underrelaxationFT_exponent);
}
}
}
}
underrelaxation_ok = false;
temp_underR[D] = underrelaxation_factor;
for (int i = 0; underrelaxation_ok == false; i++)
{
if (Math.Abs(temp_underR[D] * torque) > Math.Abs(torque_P[0]))
{
underrelaxationFT_exponent -= 1;
temp_underR[D] = underrelaxation_factor * Math.Pow(10, underrelaxationFT_exponent);
}
else
{
underrelaxation_ok = true;
if (underrelaxationFT_exponent > -0)
{
underrelaxationFT_exponent = -0;
temp_underR[D] = underrelaxation_factor * Math.Pow(10, underrelaxationFT_exponent);
}
}
}
}
double[] forces_underR = new double[D];
for (int i = 0; i < D; i++)
{
forces_underR[i] = temp_underR[i] * forces[i] + (1 - temp_underR[i]) * forces_P[0][i];
}
double torque_underR = temp_underR[D] * torque + (1 - temp_underR[D]) * torque_P[0];
this.forces_P.Insert(0, forces_underR);
forces_P.Remove(forces_P.Last());
this.torque_P.Remove(torque_P.Last());
this.torque_P.Insert(0, torque_underR);
#endregion
}
/// <summary>
///
/// </summary>
/// <param name="CellPairs">
/// 1st index: list of cells <br/>
/// 2nd index: in {0, 1}
/// </param>
/// <param name="M">
/// 1st index: corresponds with 1st index of <paramref name="CellPairs"/><br/>
/// 2nd index: matrix row index <br/>
/// 3rd index: matrix column index
/// </param>
/// <param name="Minv">the inverse of <paramref name="M"/></param>
/// <remarks>
/// Let \f$ K_j \f$ and \f$ K_i \f$ be two different cells with a linear-affine
/// transformation to the reference element.
/// Here, \f$ j \f$=<paramref name="CellPairs"/>[a,0] and \f$ i \f$=<paramref name="CellPairs"/>[a,1].
/// The DG-basis in these cells can uniquely be represented as
/// \f[
/// \phi_{j n} (\vec{x}) = p_n (\vec{x}) \vec{1}_{K_j} (\vec{x})
/// \textrm{ and }
/// \phi_{i m} (\vec{x}) = q_m (\vec{x}) \vec{1}_{K_i} (\vec{x})
/// \f]
/// where \f$ \vec{1}_X \f$ denotes the characteristic function for set \f$ X \f$
/// and \f$ p_n\f$ and \f$ p_m\f$ are polynomials.
/// Then, for the output \f$ M \f$ =<paramref name="M"/>[a,-,-] fulfills
/// \f[
/// \phi_{j n} + \sum_{m} M_{m n} \phi_{i m}
/// =
/// p_n \vec{1}_{K_j \cup K_i}
/// \f]
/// </remarks>
public void GetExtrapolationMatrices(int[,] CellPairs, MultidimensionalArray M, MultidimensionalArray Minv = null)
{
var m_Context = this.GridDat;
int N = this.Length;
int Esub = CellPairs.GetLength(0);
int JE = this.GridDat.iLogicalCells.Count;
int J = this.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (CellPairs.GetLength(1) != 2)
{
throw new ArgumentOutOfRangeException("second dimension is expected to be 2!");
}
if (M.Dimension != 3)
{
throw new ArgumentException();
}
if (M.GetLength(0) != Esub)
{
throw new ArgumentException();
}
if (M.GetLength(1) != N || M.GetLength(2) != N)
{
throw new ArgumentException();
}
if (Minv != null)
{
if (Minv.GetLength(0) != Esub)
{
throw new ArgumentException();
}
if (Minv.GetLength(1) != N || Minv.GetLength(2) != N)
{
throw new ArgumentException();
}
}
MultidimensionalArray NodesGlobal = new MultidimensionalArray(3);
MultidimensionalArray Minv_tmp = MultidimensionalArray.Create(N, N);
MultidimensionalArray M_tmp = MultidimensionalArray.Create(N, N);
for (int esub = 0; esub < Esub; esub++) // loop over the cell pairs...
{
int jCell0 = CellPairs[esub, 0];
int jCell1 = CellPairs[esub, 1];
if (jCell0 < 0 || jCell0 >= JE)
{
throw new ArgumentOutOfRangeException("Cell index out of range.");
}
if (jCell1 < 0 || jCell1 >= JE)
{
throw new ArgumentOutOfRangeException("Cell index out of range.");
}
bool swap;
if (jCell0 >= J)
{
//if(true) {
swap = true;
int a = jCell0;
jCell0 = jCell1;
jCell1 = a;
}
else
{
swap = false;
}
if (!m_Context.iGeomCells.IsCellAffineLinear(jCell0))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
if (!m_Context.iGeomCells.IsCellAffineLinear(jCell1))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
Debug.Assert(jCell0 < J);
var cellMask = new CellMask(m_Context, new[] { new Chunk()
{
i0 = jCell0, Len = 1
} }, MaskType.Geometrical);
// we project the basis function from 'jCell1' onto 'jCell0'
CellQuadrature.GetQuadrature(new int[2] {
N, N
}, m_Context,
(new CellQuadratureScheme(true, cellMask)).Compile(m_Context, this.Degree * 2), // integrate over target cell
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray _EvalResult) {
NodeSet nodes_Cell0 = QR.Nodes;
Debug.Assert(Length == 1);
NodesGlobal.Allocate(1, nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
m_Context.TransformLocal2Global(nodes_Cell0, jCell0, 1, NodesGlobal, 0);
var nodes_Cell1 = new NodeSet(GridDat.iGeomCells.GetRefElement(jCell1), nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
m_Context.TransformGlobal2Local(NodesGlobal.ExtractSubArrayShallow(0, -1, -1), nodes_Cell1, jCell1, null);
nodes_Cell1.LockForever();
var phi_0 = this.CellEval(nodes_Cell0, jCell0, 1).ExtractSubArrayShallow(0, -1, -1);
var phi_1 = this.CellEval(nodes_Cell1, jCell1, 1).ExtractSubArrayShallow(0, -1, -1);
var EvalResult = _EvalResult.ExtractSubArrayShallow(0, -1, -1, -1);
EvalResult.Multiply(1.0, phi_1, phi_0, 0.0, "kmn", "kn", "km");
},
/*_SaveIntegrationResults:*/ delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
Debug.Assert(Length == 1);
var res = ResultsOfIntegration.ExtractSubArrayShallow(0, -1, -1);
Minv_tmp.Clear();
Minv_tmp.Acc(1.0, res);
}).Execute();
// compute the inverse
Minv_tmp.InvertTo(M_tmp);
// store
if (!swap)
{
M.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, M_tmp);
if (Minv != null)
{
Minv.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, Minv_tmp);
}
}
else
{
M.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, Minv_tmp);
if (Minv != null)
{
Minv.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, M_tmp);
}
}
}
}
static internal void ComputeMassMatrixBlocks(
IEnumerable <SpeciesId> _SpeciesIds,
out Dictionary <SpeciesId, MassMatrixBlockContainer> Result,
Basis b,
XDGSpaceMetrics homie)
{
using (var tracer = new FuncTrace()) {
if (b is XDGBasis)
{
throw new ArgumentException();
}
var ctx = homie.GridDat;
Result = new Dictionary <SpeciesId, MassMatrixBlockContainer>();
var schemeHelper = homie.XQuadSchemeHelper;
int Nnx = b.Length;
int quadorder = homie.CutCellQuadOrder;
// define domains and allocate memory
// ==================================
foreach (var Species in _SpeciesIds) // loop over species...
// interation dom
{
var _IntegrationDomain = homie.LevelSetRegions.GetSpeciesMask(Species).Intersect(homie.LevelSetRegions.GetCutCellMask());
// domain for mass-matrix blocks (include agglomeration targets)
var _BlockDomain = _IntegrationDomain; //.Union(Agg.GetAgglomerator(Species).AggInfo.AllAffectedCells);
// alloc mem for blocks
var _MassMatrixBlocksSpc = MultidimensionalArray.Create(_BlockDomain.NoOfItemsLocally, Nnx, Nnx);
// Subgrid index to cell index
int[] _jSub2jCell = _BlockDomain.ItemEnum.ToArray();
// cell to subgrid index
//Dictionary<int, int> _jCell2jSub;
//if (Agg.GetAgglomerator(Species).AggInfo.AgglomerationPairs.Length > 0) {
// _jCell2jSub = new Dictionary<int, int>();
// for (int i = 0; i < _jSub2jCell.Length; i++) {
// _jCell2jSub.Add(_jSub2jCell[i], i);
// }
//} else {
// _jCell2jSub = null;
//}
Result.Add(Species, new MassMatrixBlockContainer()
{
IntegrationDomain = _IntegrationDomain,
MassMatrixBlocks = _MassMatrixBlocksSpc,
//jCell2jSub = _jCell2jSub,
jSub2jCell = _jSub2jCell
});
}
// compute blocks
// ==============
foreach (var Species in _SpeciesIds)
{
// get quad scheme
CellQuadratureScheme scheme = schemeHelper.GetVolumeQuadScheme(Species, IntegrationDomain: Result[Species].IntegrationDomain);
// result storage
var MassMatrixBlocksSpc = Result[Species].MassMatrixBlocks;
tracer.Info("mass matrix quad order: " + quadorder);
// compute the products of the basis functions:
int BlockCnt = -1;
int[] BlockCell = Result[Species].jSub2jCell;
CellMask speciesCells = homie.LevelSetRegions.GetSpeciesMask(Species);
CellQuadrature.GetQuadrature(
new int[] { Nnx, Nnx },
ctx,
scheme.Compile(ctx, quadorder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
// Del_Evaluate
// ~~~~~~~~~~~~~
var BasisVal = b.CellEval(QR.Nodes, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "ikmn", "ikm", "ikn");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
// Del_SaveIntegrationResults
// ~~~~~~~~~~~~~~~~~~~~~~~~~~
for (int i = 0; i < Length; i++)
{
int jCell = i0 + i;
BlockCnt++;
// insert ID block in agglomeration target cells (if necessary):
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
var Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
while (BlockCell[BlockCnt] < jCell)
{
// agglomeration source/target cell that is not cut
// mass matrix is identity (full) or zero (void)
Block.Clear();
if (speciesCells.Contains(BlockCell[BlockCnt]))
{
// cell is full
for (int nn = 0; nn < Nnx; nn++)
{
Block[nn, nn] = 1.0;
}
}
BlockCnt++;
Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
}
// store computed block
// - - - - - - - - - - -
Debug.Assert(BlockCell[BlockCnt] == jCell);
MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1)
.Set(ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
#if DEBUG
for (int n = 0; n < Nnx; n++)
{
for (int m = 0; m < Nnx; m++)
{
Debug.Assert(Block[n, m] == Block[m, n]);
}
}
#endif
}
}).Execute();
// ------------------------------------ quadrature end.
BlockCnt++;
while (BlockCnt < MassMatrixBlocksSpc.GetLength(0))
{
// agglomeration source/target cell that is not cut
// mass matrix is identity (full) or zero (void)
var Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
Block.Clear();
if (speciesCells.Contains(BlockCell[BlockCnt]))
{
// cell is full
for (int nn = 0; nn < Nnx; nn++)
{
Block[nn, nn] = 1.0;
}
}
BlockCnt++;
}
/*
* // test mass matrix for positive definiteness
* {
* int JSUB = MassMatrixBlocksSpc.GetLength(0);
* SubGrid Idom = null;
*
* int failCount = 0;
* var PosDefiniteTest = new FullMatrix(Nnx, Nnx);
*
* for (int jsub = 0; jsub < JSUB; jsub++) {
* PosDefiniteTest.Clear();
* PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), 1.0);
*
* try {
* PosDefiniteTest.Clear();
* PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), 1.0);
* PosDefiniteTest.InvertSymmetrical();
*
* //PosDefiniteTest.Clear();
* //PosDefiniteTest.AccEye(1.0);
* //PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), -1.0);
* //PosDefiniteTest.InvertSymmetrical();
* } catch (ArithmeticException ae) {
* if (Idom == null)
* Idom = new SubGrid(scheme.Domain);
*
* int jCell = Idom.SubgridIndex2LocalCellIndex[jsub];
* long Gid = Tracker.GridDat.Cells.GetCell(jCell).GlobalID;
*
*
* double volFrac = Tracker.GetSpeciesVolume(jCell, Species)/ctx.Cells.GetCellVolume(jCell);
*
* var errString = string.Format("Indefinite mass matrix in cell: globalId = {0}, local index = {1}, species {2}; \n cell volume fraction: {3};\n [{4}]", Gid, jCell, Tracker.GetSpeciesName(Species), volFrac, ae.Message);
* tracer.Logger.Error(errString);
* //Console.WriteLine(errString);
* failCount++;
* }
* }
*
* if (failCount > 0) {
* var errString = string.Format("Indefinite mass matrix in {0} of {1} cut cells", failCount, JSUB);
* tracer.Logger.Error(errString);
* Console.WriteLine(errString);
* } else {
* Console.WriteLine("No indefinite mass matrix blocks");
* }
*
* }
* // */
// backup before agglomeration (required if we wanna treat e.g. velocity in DG and pressure in XDG)
//MultidimensionalArray[] massMatrixBlocksB4Agglom = new MultidimensionalArray[Result[Species].jSub2jCell.Length];
//Result[Species].MassMatrixBlocks_B4Agglom = massMatrixBlocksB4Agglom;
//var _jCell2jSub = Result[Species].jCell2jSub;
//int J = ctx.Cells.NoOfLocalUpdatedCells;
//foreach (var pair in Agg.GetAgglomerator(Species).AggInfo.AgglomerationPairs) {
// foreach (int jCell in new int[] { pair.jCellSource, pair.jCellTarget }) { // create a backup of source and target cell
// if (jCell >= J)
// continue;
// int jSub = _jCell2jSub[jCell];
// if (massMatrixBlocksB4Agglom[jSub] == null) {
// massMatrixBlocksB4Agglom[jSub] = MassMatrixBlocksSpc.ExtractSubArrayShallow(jSub, -1, -1).CloneAs();
// }
// }
//}
// agglomeration
//Agg.GetAgglomerator(Species).ManipulateMassMatrixBlocks(MassMatrixBlocksSpc, b, Result[Species].jSub2jCell, Result[Species].jCell2jSub);
//throw new NotImplementedException("todo");
}
}
}
/// <summary>
/// Calculates the added damping tensor by integrating over the level set of the particle.
/// </summary>
/// <param name="particle">
/// The current particle.
/// </param>
/// <param name="levelSetTracker">
/// The level set tracker.
/// </param>
/// <param name="fluidViscosity"></param>
/// <param name="fluidDensity"></param>
/// <param name="dt"></param>
/// <param name="currentPosition"></param>
/// <returns></returns>
internal double[,] IntegrationOverLevelSet(Particle particle, LevelSetTracker levelSetTracker, double fluidViscosity, double fluidDensity, double dt, double[] currentPosition)
{
double[,] addedDampingTensor = new double[6, 6];
double alpha = 0.5;
int RequiredOrder = 2;
for (int DampingTensorID = 0; DampingTensorID < 4; DampingTensorID++)
{
for (int d1 = 0; d1 < 3; d1++)
{
for (int d2 = 0; d2 < 3; d2++)
{
void evalfD(int j0, int Len, NodeSet Ns, MultidimensionalArray result)
{
int K = result.GetLength(1);
MultidimensionalArray Normals = levelSetTracker.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
MultidimensionalArray NodeSetGlobal = Ns.CloneAs();
if (levelSetTracker.GridDat.SpatialDimension == 2)
{
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
levelSetTracker.GridDat.TransformLocal2Global(Ns, NodeSetGlobal, j0 + j);
double dh = CalculateNormalMeshSpacing(levelSetTracker, Ns, Normals, j, k);
double delta = dh * Math.Sqrt(fluidDensity) / (Math.Sqrt(alpha * fluidViscosity * dt));
double dn = dh / (1 - Math.Exp(-delta));
double[] R = new double[3];
R[0] = NodeSetGlobal[k, 0] - currentPosition[0];
R[1] = NodeSetGlobal[k, 1] - currentPosition[1];
R[2] = 0;
double[] NormalComponent = new double[3];
double test = NodeSetGlobal[k, 0];
double test2 = NodeSetGlobal[k, 1];
NormalComponent[0] = Normals[j, k, 0];
NormalComponent[1] = Normals[j, k, 1];
NormalComponent[2] = 0;
switch (DampingTensorID)
{
case 0: //D^{vv}
result[j, k] = d1 == d2 ? (1 - NormalComponent[d1] * NormalComponent[d2]) * fluidViscosity / dn : -NormalComponent[d1] * NormalComponent[d2] * fluidViscosity / dn;
break;
case 1: //D^{vw}
if (d1 == 2 && d2 != 2)
{
result[j, k] = R[1 - d2] * Math.Pow(-1, d2) * fluidViscosity / dn;
}
else if (d1 != 2 && d2 == 2)
{
result[j, k] = ((1 - NormalComponent[d1] * NormalComponent[d1]) * (-R[1 - d1]) - NormalComponent[d1] * NormalComponent[1 - d1] * R[d1]) * Math.Pow(-1, d1) * fluidViscosity / dn;
}
else
{
result[j, k] = 0;
}
break;
case 2: //D^{wv}
if (d2 == 2 && d1 != 2)
{
result[j, k] = R[1 - d1] * Math.Pow(-1, d1) * fluidViscosity / dn;
}
else if (d2 != 2 && d1 == 2)
{
result[j, k] = ((1 - NormalComponent[d2] * NormalComponent[d2]) * (-R[1 - d2]) - NormalComponent[d2] * NormalComponent[1 - d2] * R[d2]) * Math.Pow(-1, d2) * fluidViscosity / dn;
}
else
{
result[j, k] = 0;
}
break;
case 3: //D^{ww}
if (d1 == d2 && d1 != 2)
{
result[j, k] = R[1 - d1].Pow2() * fluidViscosity / dn;
}
else if (d1 != d2 && d1 != 2 && d2 != 2)
{
result[j, k] = -R[0] * R[1] * fluidViscosity / dn;
}
else if (d1 == 2 && d2 == 2)
{
result[j, k] = (((1 - NormalComponent[0] * NormalComponent[0]) * R[1] + NormalComponent[0] * NormalComponent[1] * R[0]) * R[1] + ((1 - NormalComponent[1] * NormalComponent[1]) * R[0] + NormalComponent[0] * NormalComponent[1] * R[1]) * R[0]) * fluidViscosity / dn;
}
else
{
result[j, k] = 0;
}
break;
}
}
}
}
else
{
throw new NotImplementedException("Currently the calculation of the Damping tensors is only available for 2D");
}
}
var SchemeHelper = levelSetTracker.GetXDGSpaceMetrics(new[] { levelSetTracker.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, particle.CutCells_P(levelSetTracker));
CellQuadrature.GetQuadrature(new int[] { 1 }, levelSetTracker.GridDat,
cqs.Compile(levelSetTracker.GridDat, RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
evalfD(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int l = 0; l < Length; l++)
{
switch (DampingTensorID)
{
case 0:
addedDampingTensor[d1, d2] += ResultsOfIntegration[l, 0];
break;
case 1:
addedDampingTensor[d1, d2 + 3] += ResultsOfIntegration[l, 0];
break;
case 2:
addedDampingTensor[d1 + 3, d2] += ResultsOfIntegration[l, 0];
break;
case 3:
addedDampingTensor[d1 + 3, d2 + 3] += ResultsOfIntegration[l, 0];
break;
}
}
}
).Execute();
}
}
}
if (levelSetTracker.GridDat.SpatialDimension == 2)
{
return(ModifyDampingTensor2D(addedDampingTensor));
}
else
{
throw new NotImplementedException("Currently the calculation of the Damping tensors is only available for 2D");
}
}
/// <summary>
/// Update Forces and Torque acting from fluid onto the particle
/// </summary>
/// <param name="U"></param>
/// <param name="P"></param>
/// <param name="LsTrk"></param>
/// <param name="muA"></param>
public void UpdateForcesAndTorque(VectorField <SinglePhaseField> U, SinglePhaseField P, LevelSetTracker LsTrk, double muA, double dt, double fluidDensity, bool NotFullyCoupled)
{
if (skipForceIntegration)
{
skipForceIntegration = false;
return;
}
HydrodynamicForces[0][0] = 0;
HydrodynamicForces[0][1] = 0;
HydrodynamicTorque[0] = 0;
int RequiredOrder = U[0].Basis.Degree * 3 + 2;
Console.WriteLine("Forces coeff: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
double[] Forces = new double[SpatialDim];
SinglePhaseField[] UA = U.ToArray();
ConventionalDGField pA = null;
pA = P;
if (IncludeTranslation)
{
for (int d = 0; d < SpatialDim; d++)
{
void ErrFunc(int CurrentCellID, int Length, NodeSet Ns, MultidimensionalArray result)
{
int NumberOfNodes = result.GetLength(1);
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Length, NumberOfNodes, SpatialDim, SpatialDim);
MultidimensionalArray pARes = MultidimensionalArray.Create(Length, NumberOfNodes);
var Normals = LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, CurrentCellID, Length);
for (int i = 0; i < SpatialDim; i++)
{
UA[i].EvaluateGradient(CurrentCellID, Length, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
pA.Evaluate(CurrentCellID, Length, Ns, pARes);
for (int j = 0; j < Length; j++)
{
for (int k = 0; k < NumberOfNodes; k++)
{
result[j, k] = ForceIntegration.CalculateStressTensor(Grad_UARes, pARes, Normals, muA, k, j, this.SpatialDim, d);
}
}
}
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, CutCells_P(LsTrk));
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult)
{
ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration)
{
Forces[d] = ParticleAuxillary.ForceTorqueSummationWithNeumaierArray(Forces[d], ResultsOfIntegration, Length);
}
).Execute();
}
}
double Torque = 0;
if (IncludeRotation)
{
void ErrFunc2(int j0, int Len, NodeSet Ns, MultidimensionalArray result)
{
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, SpatialDim, SpatialDim);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
// Evaluate tangential velocity to level-set surface
var Normals = LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < SpatialDim; i++)
{
UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
pA.Evaluate(j0, Len, Ns, pARes);
for (int j = 0; j < Len; j++)
{
MultidimensionalArray tempArray = Ns.CloneAs();
LsTrk.GridDat.TransformLocal2Global(Ns, tempArray, j0 + j);
for (int k = 0; k < K; k++)
{
result[j, k] = ForceIntegration.CalculateTorqueFromStressTensor2D(Grad_UARes, pARes, Normals, tempArray, muA, k, j, Position[0]);
}
}
}
var SchemeHelper2 = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs2 = SchemeHelper2.GetLevelSetquadScheme(0, CutCells_P(LsTrk));
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs2.Compile(LsTrk.GridDat, RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult)
{
ErrFunc2(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration)
{
Torque = ParticleAuxillary.ForceTorqueSummationWithNeumaierArray(Torque, ResultsOfIntegration, Length);
}
).Execute();
}
// add gravity
{
Forces[1] += (particleDensity - fluidDensity) * Area_P * GravityVertical;
}
// Sum forces and moments over all MPI processors
// ==============================================
{
int NoOfVars = 1 + SpatialDim;
double[] StateBuffer = new double[NoOfVars];
StateBuffer[0] = Torque;
for (int d = 0; d < SpatialDim; d++)
{
StateBuffer[1 + d] = Forces[d];
}
double[] GlobalStateBuffer = StateBuffer.MPISum();
Torque = GlobalStateBuffer[0];
for (int d = 0; d < SpatialDim; d++)
{
Forces[d] = GlobalStateBuffer[1 + d];
}
}
if (neglectAddedDamping == false)
{
double fest = Forces[0];
Forces[0] = Forces[0] + AddedDampingCoefficient * dt * (AddedDampingTensor[0, 0] * TranslationalAcceleration[0][0] + AddedDampingTensor[1, 0] * TranslationalAcceleration[0][1] + AddedDampingTensor[0, 2] * RotationalAcceleration[0]);
Forces[1] = Forces[1] + AddedDampingCoefficient * dt * (AddedDampingTensor[0, 1] * TranslationalAcceleration[0][0] + AddedDampingTensor[1, 1] * TranslationalAcceleration[0][1] + AddedDampingTensor[1, 2] * RotationalAcceleration[0]);
Torque += AddedDampingCoefficient * dt * (AddedDampingTensor[2, 0] * TranslationalAcceleration[0][0] + AddedDampingTensor[2, 1] * TranslationalAcceleration[0][1] + AddedDampingTensor[2, 2] * RotationalAcceleration[0]);
}
if (iteration_counter_P == -1 || NotFullyCoupled || iteration_counter_P == 250 || stupidcounter == 0)
{
Console.WriteLine();
if (iteration_counter_P == 1)
{
Console.WriteLine("First iteration of the current timestep, all relaxation factors are set to 1");
}
if (iteration_counter_P == 250)
{
Console.WriteLine("250 iterations, I'm trying to jump closer to the real solution");
}
for (int d = 0; d < SpatialDim; d++)
{
HydrodynamicForces[0][d] = 0;
if (Math.Abs(Forces[d]) < ForceAndTorque_convergence * 1e-2 && ClearSmallValues == true)
{
Forces[d] = 0;
}
HydrodynamicForces[0][d] = Forces[d];
}
HydrodynamicTorque[0] = 0;
if (Math.Abs(Torque) < ForceAndTorque_convergence * 1e-2 && ClearSmallValues == true)
{
Torque = 0;
}
HydrodynamicTorque[0] = Torque;
stupidcounter = 1;
}
else
{
double[] RelaxatedForceAndTorque = Underrelaxation.RelaxatedForcesAndTorque(Forces, Torque, ForcesPrevIteration, TorquePrevIteration, ForceAndTorque_convergence, underrelaxation_factor, ClearSmallValues, AddaptiveUnderrelaxation, AverageDistance, iteration_counter_P);
for (int d = 0; d < SpatialDim; d++)
{
HydrodynamicForces[0][d] = RelaxatedForceAndTorque[d];
}
HydrodynamicTorque[0] = RelaxatedForceAndTorque[SpatialDim];
}
//for (int d = 0; d < SpatialDim; d++)// changes sign depending on the sign of Forces[d], should increase the convergence rate. (testing needed)
//{
// if (Math.Abs(HydrodynamicForces[0][d] - Forces[0]) > Math.Abs(Forces[d]))
// {
// HydrodynamicForces[0][d] *= -1;
// }
//}
if (double.IsNaN(HydrodynamicForces[0][0]) || double.IsInfinity(HydrodynamicForces[0][0]))
{
throw new ArithmeticException("Error trying to calculate hydrodynamic forces (x). Value: " + HydrodynamicForces[0][0]);
}
if (double.IsNaN(HydrodynamicForces[0][1]) || double.IsInfinity(HydrodynamicForces[0][1]))
{
throw new ArithmeticException("Error trying to calculate hydrodynamic forces (y). Value: " + HydrodynamicForces[0][1]);
}
if (double.IsNaN(HydrodynamicTorque[0]) || double.IsInfinity(HydrodynamicTorque[0]))
{
throw new ArithmeticException("Error trying to calculate hydrodynamic torque. Value: " + HydrodynamicTorque[0]);
}
}
private void ComputeAverageU <T>(IEnumerable <T> U0, VectorField <XDGField> U0mean, int order, XQuadSchemeHelper qh) where T : DGField
{
using (FuncTrace ft = new FuncTrace()) {
var CC = this.LsTrk.Regions.GetCutCellMask();
int D = this.LsTrk.GridDat.SpatialDimension;
double minvol = Math.Pow(this.LsTrk.GridDat.Cells.h_minGlobal, D);
//var qh = new XQuadSchemeHelper(agg);
foreach (var Spc in this.LsTrk.SpeciesIdS) // loop over species...
//var Spc = this.LsTrk.GetSpeciesId("B"); {
// shadow fields
{
DGField[] U0_Spc = U0.Select(U0_d => (U0_d is XDGField) ? ((DGField)((U0_d as XDGField).GetSpeciesShadowField(Spc))) : ((DGField)U0_d)).ToArray();
var U0mean_Spc = U0mean.Select(U0mean_d => U0mean_d.GetSpeciesShadowField(Spc)).ToArray();
// normal cells:
for (int d = 0; d < D; d++)
{
U0mean_Spc[d].AccLaidBack(1.0, U0_Spc[d], this.LsTrk.Regions.GetSpeciesMask(Spc));
}
// cut cells
var scheme = qh.GetVolumeQuadScheme(Spc, IntegrationDomain: this.LsTrk.Regions.GetCutCellMask());
var rule = scheme.Compile(this.LsTrk.GridDat, order);
CellQuadrature.GetQuadrature(new int[] { D + 1 }, // vector components: ( avg_vel[0], ... , avg_vel[D-1], cell_volume )
this.LsTrk.GridDat,
rule,
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.Clear();
for (int d = 0; d < D; d++)
{
U0_Spc[d].Evaluate(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, d));
}
var Vol = EvalResult.ExtractSubArrayShallow(-1, -1, D);
Vol.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
int jCell = i + i0;
double Volume = ResultsOfIntegration[i, D];
if (Math.Abs(Volume) < minvol * 1.0e-12)
{
// keep current value
// since the volume of species 'Spc' in cell 'jCell' is 0.0, the value in this cell should have no effect
}
else
{
for (int d = 0; d < D; d++)
{
double IntVal = ResultsOfIntegration[i, d];
U0mean_Spc[d].SetMeanValue(jCell, IntVal / Volume);
}
}
}
}).Execute();
}
#if DEBUG
{
var Uncut = LsTrk.Regions.GetCutCellMask().Complement();
VectorField <SinglePhaseField> U0mean_check = new VectorField <SinglePhaseField>(D, new Basis(LsTrk.GridDat, 0), SinglePhaseField.Factory);
for (int d = 0; d < D; d++)
{
U0mean_check[d].ProjectField(1.0, U0.ElementAt(d).Evaluate,
new CellQuadratureScheme(false, Uncut).AddFixedOrderRules(LsTrk.GridDat, U0.ElementAt(d).Basis.Degree + 1));
}
foreach (var _Spc in this.LsTrk.SpeciesIdS) // loop over species...
{
for (int d = 0; d < D; d++)
{
U0mean_check[d].AccLaidBack(-1.0, U0mean[d].GetSpeciesShadowField(_Spc), Uncut.Intersect(LsTrk.Regions.GetSpeciesMask(_Spc)));
}
}
double checkNorm = U0mean_check.L2Norm();
Debug.Assert(checkNorm < 1.0e-6);
}
#endif
U0mean.ForEach(F => F.CheckForNanOrInf(true, true, true));
}
}
private double[] ComputeBenchmarkQuantities()
{
int order = 0;
if (CorrectionLsTrk.GetCachedOrders().Count > 0)
{
order = CorrectionLsTrk.GetCachedOrders().Max();
}
else
{
order = 1;
}
var SchemeHelper = CorrectionLsTrk.GetXDGSpaceMetrics(CorrectionLsTrk.SpeciesIdS.ToArray(), order, 1).XQuadSchemeHelper;
// area of bubble
double area = 0.0;
SpeciesId spcId = CorrectionLsTrk.SpeciesIdS[1];
var vqs = SchemeHelper.GetVolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, CorrectionLsTrk.GridDat,
vqs.Compile(CorrectionLsTrk.GridDat, order),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
area += ResultsOfIntegration[i, 0];
}
}
).Execute();
area = area.MPISum();
// surface
double surface = 0.0;
//CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
var surfElemVol = SchemeHelper.Get_SurfaceElement_VolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, CorrectionLsTrk.GridDat,
surfElemVol.Compile(CorrectionLsTrk.GridDat, this.m_HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
surface += ResultsOfIntegration[i, 0];
}
}
).Execute();
surface = surface.MPISum();
// circularity
double diamtr_c = Math.Sqrt(4 * area / Math.PI);
double perimtr_b = surface;
double circ = Math.PI * diamtr_c / perimtr_b;
// total concentration, careful above values are "old" when CorrectionTracker is not updated, this value is always "new"
double concentration = 0.0;
var tqs = new CellQuadratureScheme();
CellQuadrature.GetQuadrature(new int[] { 1 }, phi.GridDat,
tqs.Compile(phi.GridDat, phi.Basis.Degree * 2 + 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
phi.Evaluate(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
concentration += ResultsOfIntegration[i, 0];
}
}
).Execute();
concentration = concentration.MPISum();
// total mixing energy
double energy = 0.0;
var eqs = new CellQuadratureScheme();
int D = phi.GridDat.SpatialDimension;
SinglePhaseField[] PhiGrad = new SinglePhaseField[D];
for (int d = 0; d < D; d++)
{
PhiGrad[d] = new SinglePhaseField(phi.Basis, string.Format("G_{0}", d));
PhiGrad[d].Derivative(1.0, phi, d);
}
MultidimensionalArray _Phi = new MultidimensionalArray(2);
MultidimensionalArray _GradPhi = new MultidimensionalArray(3);
MultidimensionalArray _NormGrad = new MultidimensionalArray(2);
CellQuadrature.GetQuadrature(new int[] { 1 }, phi.GridDat,
eqs.Compile(phi.GridDat, phi.Basis.Degree * 2 + 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
int K = EvalResult.GetLength(1);
// alloc buffers
// -------------
if (_Phi.GetLength(0) != Length || _Phi.GetLength(1) != K)
{
_Phi.Allocate(Length, K);
_GradPhi.Allocate(Length, K, D);
_NormGrad.Allocate(Length, K);
}
else
{
_Phi.Clear();
_GradPhi.Clear();
_NormGrad.Clear();
}
// chemical potential
phi.Evaluate(i0, Length, QR.Nodes, _Phi.ExtractSubArrayShallow(-1, -1));
_Phi.ApplyAll(x => 0.25 / (this.Control.cahn.Pow2()) * (x.Pow2() - 1.0).Pow2());
for (int d = 0; d < D; d++)
{
PhiGrad[d].Evaluate(i0, Length, QR.Nodes, _GradPhi.ExtractSubArrayShallow(-1, -1, d));
}
// free surface energy
for (int d = 0; d < D; d++)
{
var GradPhi_d = _GradPhi.ExtractSubArrayShallow(-1, -1, d);
_NormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
_NormGrad.ApplyAll(x => 0.5 * x);
EvalResult.ExtractSubArrayShallow(-1, -1, 0).Acc(1.0, _Phi);
EvalResult.ExtractSubArrayShallow(-1, -1, 0).Acc(1.0, _NormGrad);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
energy += ResultsOfIntegration[i, 0];
}
}
).Execute();
energy = energy.MPISum();
// replace 1.96 (RB_TC2) with actual surface tension
// see Yue (2004)
double lambda = this.Control.cahn.Pow2() * 1.96 * surface / energy;
return(new double[] { area, surface, circ, concentration, energy, lambda, this.Control.diff });
}
/// <summary>
/// Calculates the Torque around the center of mass
/// </summary>
/// <param name="U"></param>
/// <param name="P"></param>
/// <param name="muA"></param>
/// <param name="particleRadius"></param>
/// <returns></returns>
static public double GetTorque(VectorField <SinglePhaseField> U, SinglePhaseField P,
LevelSetTracker LsTrk,
double muA, double particleRadius)
{
var _LsTrk = LsTrk;
int D = _LsTrk.GridDat.SpatialDimension;
var UA = U.ToArray();
//if (D > 2) throw new NotImplementedException("Currently only 2D cases supported");
int RequiredOrder = U[0].Basis.Degree * 3;
//if (RequiredOrder > agg.HMForder)
// throw new ArgumentException();
Console.WriteLine("Torque coeff: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
ConventionalDGField pA = null;
double force = new double();
pA = P;
ScalarFunctionEx ErrFunc = delegate(int j0, int Len, NodeSet Ns, MultidimensionalArray result) {
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, D, D);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
// Evaluate tangential velocity to level-set surface
var Normals = _LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < D; i++)
{
UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
pA.Evaluate(j0, Len, Ns, pARes);
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
double acc2 = 0.0;
// Calculate the torque around a circular particle with a given radius (Paper Wan and Turek 2005)
acc += pARes[j, k] * Normals[j, k, 0];
acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
acc *= -Normals[j, k, 1] * particleRadius;
acc2 += pARes[j, k] * Normals[j, k, 1];
acc2 -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc2 -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc2 -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
acc2 *= Normals[j, k, 0] * particleRadius;
result[j, k] = acc + acc2;
}
}
};
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
//var SchemeHelper = new XQuadSchemeHelper(_LsTrk, momentFittingVariant, _LsTrk.GetSpeciesId("A"));
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, _LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, _LsTrk.GridDat,
cqs.Compile(_LsTrk.GridDat, RequiredOrder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
force += ResultsOfIntegration[i, 0];
}
}
).Execute();
return(force);
}
/// <summary>
/// ctor.
/// </summary>
public NECQuadratureVolume(IGridData context,
SpatialOperator DiffOp,
IList <DGField> _DomainFields,
IList <DGField> _ParameterFields,
UnsetteledCoordinateMapping CodomainMapping,
ICompositeQuadRule <QuadRule> domNrule)
: base(context, DiffOp, _DomainFields, _ParameterFields, CodomainMapping)
{
// -----------------
// quadrature object
// -----------------
m_Quad = CellQuadrature.GetQuadrature2(new int[] { CodomainMapping.NoOfCoordinatesPerCell }, context, domNrule,
this.EvaluateEx,
this.SaveIntegrationResults,
this.AllocateBuffers);
int Gamma = _DomainFields.Count;
// ------------------------
// sort equation components
// ------------------------
m_NonlinSources = EquationComponentArgMapping <INonlinearSource> .GetArgMapping(DiffOp, true);
m_NonlinFormV = EquationComponentArgMapping <INonlinVolumeForm_V> .GetArgMapping(DiffOp, true,
eq => ((eq.VolTerms & (TermActivationFlags.V | TermActivationFlags.UxV | TermActivationFlags.GradUxV)) != 0),
eq => (eq is IVolumeForm ? new NonlinVolumeFormVectorizer((IVolumeForm)eq) : null));
m_NonlinFormGradV = EquationComponentArgMapping <INonlinVolumeForm_GradV> .GetArgMapping(DiffOp, true,
eq => ((eq.VolTerms & (TermActivationFlags.UxGradV | TermActivationFlags.GradV | TermActivationFlags.GradUxGradV)) != 0),
eq => (eq is IVolumeForm ? new NonlinVolumeFormVectorizer((IVolumeForm)eq) : null));
Debug.Assert(base.m_DomainFields.Length >= Gamma);
m_ValueRequired = new bool[base.m_DomainFields.Length];
m_GradientRequired = new bool[Gamma];
// base.m_DomainFields may also contain parameter fields:
for (int i = Gamma; i < base.m_DomainFields.Length; i++)
{
m_ValueRequired[i] = true;
}
this.m_NonlinFormV.DetermineReqFields(m_GradientRequired,
comp => ((comp.VolTerms & (TermActivationFlags.GradUxGradV | TermActivationFlags.GradUxV)) != 0));
this.m_NonlinFormGradV.DetermineReqFields(m_GradientRequired,
comp => ((comp.VolTerms & (TermActivationFlags.GradUxGradV | TermActivationFlags.GradUxV)) != 0));
this.m_NonlinFormV.DetermineReqFields(m_ValueRequired,
comp => ((comp.VolTerms & (TermActivationFlags.UxGradV | TermActivationFlags.UxV)) != 0));
this.m_NonlinFormGradV.DetermineReqFields(m_ValueRequired,
comp => ((comp.VolTerms & (TermActivationFlags.UxGradV | TermActivationFlags.UxV)) != 0));
this.m_NonlinSources.DetermineReqFields(m_ValueRequired, comp => true);
base.m_NonlinFluxes.DetermineReqFields(m_ValueRequired, comp => true);
base.m_NonlinFluxesEx.DetermineReqFields(m_ValueRequired, comp => true);
// ---------
// profiling
// ---------
var _CustomTimers = new Stopwatch[] { new Stopwatch(), new Stopwatch(), new Stopwatch(), new Stopwatch(), new Stopwatch(), new Stopwatch() };
var _CustomTimers_Names = new string[] { "Flux-Eval", "Basis-Eval", "Field-Eval", "Loops", "ParametersAndNormals", "Flux-Trafo" };
Flux_Eval = _CustomTimers[0];
Flux_Trafo = _CustomTimers[5];
Field_Eval = _CustomTimers[2];
Basis_Eval = _CustomTimers[1];
Loops = _CustomTimers[3];
ParametersAndNormals = _CustomTimers[4];
m_Quad.CustomTimers = m_Quad.CustomTimers.Cat(_CustomTimers);
m_Quad.CustomTimers_Names = m_Quad.CustomTimers_Names.Cat(_CustomTimers_Names);
m_Quad.CustomTimers_RootPointer = new int[_CustomTimers_Names.Length];
ArrayTools.SetAll(m_Quad.CustomTimers_RootPointer, -1);
this.m_NonlinSources_watch = this.m_NonlinSources.InitStopWatches(0, m_Quad);
this.m_NonlinFormV_watch = this.m_NonlinFormV.InitStopWatches(0, m_Quad);
this.m_NonlinFormGradV_watch = this.m_NonlinFormGradV.InitStopWatches(0, m_Quad);
base.m_NonlinFluxesWatches = base.m_NonlinFluxes.InitStopWatches(0, m_Quad);
base.m_NonlinFluxesExWatches = base.m_NonlinFluxesEx.InitStopWatches(0, m_Quad);
// ---------------------
// alloc multidim arrays
// ---------------------
m_FluxValues = new MultidimensionalArray[m_CodomainBasisS.Length];
m_FluxValuesTrf = new MultidimensionalArray[m_CodomainBasisS.Length];
for (int i = 0; i < m_FluxValues.Length; i++)
{
if (m_NonlinFluxes[i].m_AllComponentsOfMyType.Length > 0 || m_NonlinFluxesEx[i].m_AllComponentsOfMyType.Length > 0 || m_NonlinFormGradV[i].m_AllComponentsOfMyType.Length > 0)
{
m_FluxValues[i] = new MultidimensionalArray(3);
m_FluxValuesTrf[i] = new MultidimensionalArray(3);
Basis GradBasis = base.m_CodomainBasisS[i];
if (m_MaxCodBasis_Gradient == null || m_MaxCodBasis_Gradient.Degree < GradBasis.Degree)
{
m_MaxCodBasis_Gradient = GradBasis;
}
}
}
m_SourceValues = new MultidimensionalArray[m_CodomainBasisS.Length];
for (int i = 0; i < m_SourceValues.Length; i++)
{
if (m_NonlinSources[i].m_AllComponentsOfMyType.Length > 0 || m_NonlinFormV[i].m_AllComponentsOfMyType.Length > 0)
{
m_SourceValues[i] = new MultidimensionalArray(2);
Basis ValBasis = base.m_CodomainBasisS[i];
if (m_MaxCodBasis == null || m_MaxCodBasis.Degree < ValBasis.Degree)
{
m_MaxCodBasis = ValBasis;
}
}
}
m_FieldValues = new MultidimensionalArray[m_DomainFields.Length];
m_FieldGradients = new MultidimensionalArray[Gamma];
for (int i = 0; i < m_DomainFields.Length; i++)
{
if (m_ValueRequired[i])
{
m_FieldValues[i] = new MultidimensionalArray(2);
}
if (i < Gamma && m_GradientRequired[i])
{
m_FieldGradients[i] = new MultidimensionalArray(3);
}
}
m_TestFuncWeighted = new MultidimensionalArray(2);
m_TestFuncGradWeighted = new MultidimensionalArray(3);
}
static public double[] GetParticleForces(VectorField <SinglePhaseField> U, SinglePhaseField P,
LevelSetTracker LsTrk,
double muA)
{
int D = LsTrk.GridDat.SpatialDimension;
// var UA = U.Select(u => u.GetSpeciesShadowField("A")).ToArray();
var UA = U.ToArray();
int RequiredOrder = U[0].Basis.Degree * 3 + 2;
//int RequiredOrder = LsTrk.GetXQuadFactoryHelper(momentFittingVariant).GetCachedSurfaceOrders(0).Max();
//Console.WriteLine("Order reduction: {0} -> {1}", _RequiredOrder, RequiredOrder);
//if (RequiredOrder > agg.HMForder)
// throw new ArgumentException();
Console.WriteLine("Forces coeff: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
ConventionalDGField pA = null;
//pA = P.GetSpeciesShadowField("A");
pA = P;
double[] forces = new double[D];
for (int d = 0; d < D; d++)
{
ScalarFunctionEx ErrFunc = delegate(int j0, int Len, NodeSet Ns, MultidimensionalArray result) {
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_UARes = MultidimensionalArray.Create(Len, K, D, D);;
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
// Evaluate tangential velocity to level-set surface
var Normals = LsTrk.DataHistories[0].Current.GetLevelSetNormals(Ns, j0, Len);
for (int i = 0; i < D; i++)
{
UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
pA.Evaluate(j0, Len, Ns, pARes);
if (LsTrk.GridDat.SpatialDimension == 2)
{
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
// pressure
switch (d)
{
case 0:
acc += pARes[j, k] * Normals[j, k, 0];
acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
break;
case 1:
acc += pARes[j, k] * Normals[j, k, 1];
acc -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
break;
default:
throw new NotImplementedException();
}
result[j, k] = acc;
}
}
}
else
{
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
// pressure
switch (d)
{
case 0:
acc += pARes[j, k] * Normals[j, k, 0];
acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 2] * Normals[j, k, 2];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 2, 0] * Normals[j, k, 2];
break;
case 1:
acc += pARes[j, k] * Normals[j, k, 1];
acc -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 1, 2] * Normals[j, k, 2];
acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 2, 1] * Normals[j, k, 2];
break;
case 2:
acc += pARes[j, k] * Normals[j, k, 2];
acc -= (2 * muA) * Grad_UARes[j, k, 2, 2] * Normals[j, k, 2];
acc -= (muA) * Grad_UARes[j, k, 2, 0] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 2, 1] * Normals[j, k, 1];
acc -= (muA) * Grad_UARes[j, k, 0, 2] * Normals[j, k, 0];
acc -= (muA) * Grad_UARes[j, k, 1, 2] * Normals[j, k, 1];
break;
default:
throw new NotImplementedException();
}
result[j, k] = acc;
}
}
}
};
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
//var SchemeHelper = new XQuadSchemeHelper(LsTrk, momentFittingVariant, );
CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
CellQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
cqs.Compile(LsTrk.GridDat, RequiredOrder), // agg.HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
forces[d] += ResultsOfIntegration[i, 0];
}
}
).Execute();
}
for (int i = 0; i < D; i++)
{
forces[i] = MPI.Wrappers.MPIExtensions.MPISum(forces[i]);
}
return(forces);
}
/// <summary>
/// computes derivatives in various ways and compares them against known values.
/// </summary>
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
base.EndTime = 0.0;
base.NoOfTimesteps = 0;
int D = this.GridData.SpatialDimension;
int J = this.GridData.iLogicalCells.NoOfLocalUpdatedCells;
Console.WriteLine("DerivativeTest.exe, test case #" + GRID_CASE + " ******************************");
//var Fix = this.GridData.iGeomEdges.FaceIndices;
//for(int iEdge = 0; iEdge < Fix.GetLength(0); iEdge++) {
// Debug.Assert(Fix[iEdge, 0] >= 0);
// Debug.Assert(Fix[iEdge, 1] >= 0);
//}
// sealing test
// =================
if (this.GridData is Foundation.Grid.Classic.GridData)
{
TestSealing(this.GridData);
}
// cell volume and edge area check, if possible
// ===============================================
if (this.CellVolume > 0)
{
double err = 0;
double Treshold = 1.0e-10;
for (int j = 0; j < J; j++)
{
err += Math.Abs(this.GridData.iLogicalCells.GetCellVolume(j) - this.CellVolume);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Cell volume error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
if (this.EdgeArea > 0)
{
double err = 0;
double Treshold = 1.0e-10;
int E = this.GridData.iLogicalEdges.Count;
for (int e = 0; e < E; e++)
{
err += Math.Abs(this.GridData.iLogicalEdges.GetEdgeArea(e) - this.EdgeArea);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Edge area error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
// Orthonormality of basis in physical coords
// ==========================================
{
Basis Bs = this.f1.Basis;
int N = Bs.Length;
int degQuad = this.GridData.iLogicalCells.GetInterpolationDegree(0) * D + Bs.Degree + 3;
int[] jG2jL = this.GridData.iGeomCells.GeomCell2LogicalCell;
// mass matrix: should be identity!
MultidimensionalArray MassMatrix = MultidimensionalArray.Create(J, N, N);
// compute mass matrix by quadrature.
var quad = CellQuadrature.GetQuadrature(new int[] { N, N }, base.GridData,
(new CellQuadratureScheme()).Compile(base.GridData, degQuad),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
NodeSet QuadNodes = QR.Nodes;
MultidimensionalArray BasisVals = Bs.CellEval(QuadNodes, i0, Length);
EvalResult.Multiply(1.0, BasisVals, BasisVals, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
if (jG2jL != null)
{
for (int i = 0; i < Length; i++)
{
int jG = i + i0;
MassMatrix.ExtractSubArrayShallow(jG2jL[jG], -1, -1)
.Acc(1.0, ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
}
}
else
{
MassMatrix.SetSubArray(ResultsOfIntegration, new int[] { i0, 0, 0 }, new int[] { i0 + Length - 1, N - 1, N - 1 });
}
},
cs: CoordinateSystem.Physical);
quad.Execute();
// check that mass matrix is Id.
int MaxErrorCell = -1;
double MaxError = -1;
for (int j = 0; j < J; j++)
{
MultidimensionalArray MassMatrix_j = MassMatrix.ExtractSubArrayShallow(j, -1, -1);
MassMatrix_j.AccEye(-1.0);
double Norm_j = MassMatrix_j.InfNorm();
if (Norm_j > MaxError)
{
MaxError = Norm_j;
MaxErrorCell = j;
}
}
bool passed = (MaxError < 1.0e-8);
m_passed = m_passed && passed;
Console.WriteLine("Mass Matrix, maximum error in Cell #" + MaxErrorCell + ", mass matrix error norm: " + MaxError + " passed? " + passed);
}
// Broken Derivatives
// =================
double totalVolume = (new SubGrid(CellMask.GetFullMask(this.GridData))).Volume;
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].Derivative(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].Derivative(1.0, f2, d);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Broken Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Flux Derivatives
// =================
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].DerivativeByFlux(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].DerivativeByFlux(1.0, f2, d);
f1Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
f2Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Linear flux Derivatives
// =======================
for (int d = 0; d < D; d++)
{
double[] korrekto = f1Gradient_Numerical[d].CoordinateVector.ToArray();
// compute
DerivativeByFluxLinear(f1, f1Gradient_Numerical[d], d, f1);
DerivativeByFluxLinear(f2, f2Gradient_Numerical[d], d, f2);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Linear Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, nonlinear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
Laplace.Evaluate(new DGField[] { this.f1 }, new DGField[] { this.Laplace_f1_Numerical });
Laplace.Evaluate(new DGField[] { this.f2 }, new DGField[] { this.Laplace_f2_Numerical });
double Treshold = 1.0e-8;
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf2, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, linear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
var LaplaceMtx = new BlockMsrMatrix(this.f1.Mapping, this.Laplace_f1_Numerical.Mapping);
var LaplaceAffine = new double[LaplaceMtx.RowPartitioning.LocalLength];
Laplace.ComputeMatrix(this.f1.Mapping, null, this.Laplace_f1_Numerical.Mapping,
LaplaceMtx, LaplaceAffine, false);
this.Laplace_f1_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f1.CoordinateVector, 1.0, this.Laplace_f1_Numerical.CoordinateVector);
this.Laplace_f2_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f2.CoordinateVector, 1.0, this.Laplace_f2_Numerical.CoordinateVector);
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double Treshold = 1.0e-8;
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf2, passed));
// comparison of finite difference Jacobian and Operator matrix
if (TestFDJacobian)
{
this.f1.Clear();
var FDJbuilder = Laplace.GetFDJacobianBuilder(this.f1.Mapping.Fields, null, this.f1.Mapping,
delegate(IEnumerable <DGField> U0, IEnumerable <DGField> Params) {
return;
});
var CheckMatrix = new BlockMsrMatrix(FDJbuilder.CodomainMapping, FDJbuilder.DomainMapping);
var CheckAffine = new double[FDJbuilder.CodomainMapping.LocalLength];
FDJbuilder.ComputeMatrix(CheckMatrix, CheckAffine);
var ErrMatrix = LaplaceMtx.CloneAs();
var ErrAffine = LaplaceAffine.CloneAs();
ErrMatrix.Acc(-1.0, CheckMatrix);
ErrAffine.AccV(-1.0, CheckAffine);
double LinfMtx = ErrMatrix.InfNorm();
double L2Aff = ErrAffine.L2NormPow2().MPISum().Sqrt();
bool passed1 = (LinfMtx < 1.0e-3);
bool passed2 = (L2Aff < Treshold);
Console.WriteLine("Finite Difference Jacobian: Matrix/Affine delta norm {0} {1}, passed? {2} {3}", LinfMtx, L2Aff, passed1, passed2);
m_passed = m_passed && passed1;
m_passed = m_passed && passed2;
}
Console.WriteLine("--------------------------------------------");
}
// finally...
// =================
if (m_passed)
{
Console.WriteLine("All tests passed. *****************************");
}
else
{
Console.WriteLine("Some error above threshold. *******************");
}
return(0.0); // return some artificial timestep
}