/// <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>
///
/// </summary>
public void AssembleMatrix_Timestepper <T>(
int CutCellQuadOrder,
BlockMsrMatrix OpMatrix, double[] OpAffine,
Dictionary <SpeciesId, MultidimensionalArray> AgglomeratedCellLengthScales,
IEnumerable <T> CurrentState,
VectorField <SinglePhaseField> SurfaceForce,
VectorField <SinglePhaseField> LevelSetGradient, SinglePhaseField ExternalyProvidedCurvature,
UnsetteledCoordinateMapping RowMapping, UnsetteledCoordinateMapping ColMapping,
double time, IEnumerable <T> CoupledCurrentState = null, IEnumerable <T> CoupledParams = null) where T : DGField
{
if (ColMapping.BasisS.Count != this.Op.DomainVar.Count)
{
throw new ArgumentException();
}
if (RowMapping.BasisS.Count != this.Op.CodomainVar.Count)
{
throw new ArgumentException();
}
// check:
var Tracker = this.LsTrk;
int D = Tracker.GridDat.SpatialDimension;
if (CurrentState != null && CurrentState.Count() != (D + 1))
{
throw new ArgumentException();
}
if (OpMatrix == null && CurrentState == null)
{
throw new ArgumentException();
}
DGField[] U0;
if (CurrentState != null)
{
U0 = CurrentState.Take(D).ToArray();
}
else
{
U0 = null;
}
LevelSet Phi = (LevelSet)(Tracker.LevelSets[0]);
SpeciesId[] SpcToCompute = AgglomeratedCellLengthScales.Keys.ToArray();
IDictionary <SpeciesId, MultidimensionalArray> InterfaceLengths = this.LsTrk.GetXDGSpaceMetrics(this.LsTrk.SpeciesIdS.ToArray(), CutCellQuadOrder).CutCellMetrics.InterfaceArea;
// advanced settings for the navier slip boundary condition
// ========================================================
CellMask SlipArea;
switch (this.dntParams.GNBC_Localization)
{
case NavierSlip_Localization.Bulk: {
SlipArea = this.LsTrk.GridDat.BoundaryCells.VolumeMask;
break;
}
case NavierSlip_Localization.ContactLine: {
SlipArea = null;
break;
}
case NavierSlip_Localization.Nearband: {
SlipArea = this.LsTrk.GridDat.BoundaryCells.VolumeMask.Intersect(this.LsTrk.Regions.GetNearFieldMask(this.LsTrk.NearRegionWidth));
break;
}
case NavierSlip_Localization.Prescribed: {
throw new NotImplementedException();
}
default:
throw new ArgumentException();
}
MultidimensionalArray SlipLengths;
SlipLengths = this.LsTrk.GridDat.Cells.h_min.CloneAs();
SlipLengths.Clear();
//SlipLengths.AccConstant(-1.0);
if (SlipArea != null)
{
foreach (Chunk cnk in SlipArea)
{
for (int i = cnk.i0; i < cnk.JE; i++)
{
switch (this.dntParams.GNBC_SlipLength)
{
case NavierSlip_SlipLength.hmin_DG: {
int degU = ColMapping.BasisS.ToArray()[0].Degree;
SlipLengths[i] = this.LsTrk.GridDat.Cells.h_min[i] / (degU + 1);
break;
}
case NavierSlip_SlipLength.hmin_Grid: {
SlipLengths[i] = SlipLengths[i] = this.LsTrk.GridDat.Cells.h_min[i];
break;
}
case NavierSlip_SlipLength.Prescribed_SlipLength: {
SlipLengths[i] = this.physParams.sliplength;
break;
}
case NavierSlip_SlipLength.Prescribed_Beta: {
SlipLengths[i] = -1.0;
break;
}
}
}
}
}
// parameter assembly
// ==================
// normals:
SinglePhaseField[] Normals; // Normal vectors: length not normalized - will be normalized at each quad node within the flux functions.
if (this.NormalsRequired)
{
if (LevelSetGradient == null)
{
LevelSetGradient = new VectorField <SinglePhaseField>(D, Phi.Basis, SinglePhaseField.Factory);
LevelSetGradient.Gradient(1.0, Phi);
}
Normals = LevelSetGradient.ToArray();
}
else
{
Normals = new SinglePhaseField[D];
}
// curvature:
SinglePhaseField Curvature;
if (this.CurvatureRequired)
{
Curvature = ExternalyProvidedCurvature;
}
else
{
Curvature = null;
}
// linearization velocity:
DGField[] U0_U0mean;
if (this.U0meanrequired)
{
XDGBasis U0meanBasis = new XDGBasis(Tracker, 0);
VectorField <XDGField> U0mean = new VectorField <XDGField>(D, U0meanBasis, "U0mean_", XDGField.Factory);
U0_U0mean = ArrayTools.Cat <DGField>(U0, U0mean);
}
else
{
U0_U0mean = new DGField[2 * D];
}
// Temperature gradient for evaporation
VectorField <DGField> GradTemp = new VectorField <DGField>(D, U0[0].Basis, XDGField.Factory);
if (CoupledCurrentState != null)
{
DGField Temp = CoupledCurrentState.ToArray()[0];
GradTemp = new VectorField <DGField>(D, Temp.Basis, "GradTemp", XDGField.Factory);
XNSEUtils.ComputeGradientForParam(Temp, GradTemp, this.LsTrk);
}
// concatenate everything
var Params = ArrayTools.Cat <DGField>(
U0_U0mean,
Curvature,
((SurfaceForce != null) ? SurfaceForce.ToArray() : new SinglePhaseField[D]),
Normals,
((evaporation) ? GradTemp.ToArray() : new SinglePhaseField[D]),
((evaporation) ? CoupledCurrentState.ToArray <DGField>() : new SinglePhaseField[1]),
((evaporation) ? CoupledParams.ToArray <DGField>() : new SinglePhaseField[1])); //((evaporation) ? GradTemp.ToArray() : new SinglePhaseField[D]));
// linearization velocity:
if (this.U0meanrequired)
{
VectorField <XDGField> U0mean = new VectorField <XDGField>(U0_U0mean.Skip(D).Take(D).Select(f => ((XDGField)f)).ToArray());
U0mean.Clear();
if (this.physParams.IncludeConvection)
{
ComputeAverageU(U0, U0mean, CutCellQuadOrder, LsTrk.GetXDGSpaceMetrics(SpcToCompute, CutCellQuadOrder, 1).XQuadSchemeHelper);
}
}
// assemble the matrix & affine vector
// ===================================
// compute matrix
if (OpMatrix != null)
{
//Op.ComputeMatrixEx(Tracker,
// ColMapping, Params, RowMapping,
// OpMatrix, OpAffine, false, time, true,
// AgglomeratedCellLengthScales,
// InterfaceLengths, SlipLengths,
// SpcToCompute);
XSpatialOperatorMk2.XEvaluatorLinear mtxBuilder = Op.GetMatrixBuilder(LsTrk, ColMapping, Params, RowMapping, SpcToCompute);
foreach (var kv in AgglomeratedCellLengthScales)
{
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].CellLengthScales = kv.Value;
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("SlipLengths", SlipLengths);
}
if (Op.SurfaceElementOperator.TotalNoOfComponents > 0)
{
foreach (var kv in InterfaceLengths)
{
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("InterfaceLengths", kv.Value);
}
}
mtxBuilder.time = time;
mtxBuilder.ComputeMatrix(OpMatrix, OpAffine);
}
else
{
XSpatialOperatorMk2.XEvaluatorNonlin eval = Op.GetEvaluatorEx(Tracker,
CurrentState.ToArray(), Params, RowMapping,
SpcToCompute);
foreach (var kv in AgglomeratedCellLengthScales)
{
eval.SpeciesOperatorCoefficients[kv.Key].CellLengthScales = kv.Value;
eval.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("SlipLengths", SlipLengths);
}
if (Op.SurfaceElementOperator.TotalNoOfComponents > 0)
{
foreach (var kv in InterfaceLengths)
{
eval.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("InterfaceLengths", kv.Value);
}
}
eval.time = time;
eval.Evaluate(1.0, 1.0, OpAffine);
#if DEBUG
// remark: remove this piece in a few months from now on (09may18) if no problems occur
//{
// BlockMsrMatrix checkOpMatrix = new BlockMsrMatrix(RowMapping, ColMapping);
// double[] checkAffine = new double[OpAffine.Length];
// Op.ComputeMatrixEx(Tracker,
// ColMapping, Params, RowMapping,
// OpMatrix, OpAffine, false, time, true,
// AgglomeratedCellLengthScales,
// InterfaceLengths, SlipLengths,
// SpcToCompute);
// double[] checkResult = checkAffine.CloneAs();
// var currentVec = new CoordinateVector(CurrentState.ToArray());
// checkOpMatrix.SpMV(1.0, new CoordinateVector(CurrentState.ToArray()), 1.0, checkResult);
// double L2_dist = GenericBlas.L2DistPow2(checkResult, OpAffine).MPISum().Sqrt();
// double RefNorm = (new double[] { checkResult.L2NormPow2(), OpAffine.L2NormPow2(), currentVec.L2NormPow2() }).MPISum().Max().Sqrt();
// Assert.LessOrEqual(L2_dist, RefNorm * 1.0e-6);
// Debug.Assert(L2_dist < RefNorm * 1.0e-6);
//}
#endif
}
// check
// =====
/*
* {
* DGField[] testDomainFieldS = ColMapping.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
* CoordinateVector test = new CoordinateVector(testDomainFieldS);
*
* DGField[] errFieldS = ColMapping.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
* CoordinateVector Err = new CoordinateVector(errFieldS);
*
* var eval = Op.GetEvaluatorEx(LsTrk,
* testDomainFieldS, Params, RowMapping);
*
* foreach (var s in this.LsTrk.SpeciesIdS)
* eval.SpeciesOperatorCoefficients[s].CellLengthScales = AgglomeratedCellLengthScales[s];
*
* eval.time = time;
* int L = test.Count;
* Random r = new Random();
* for(int i = 0; i < L; i++) {
* test[i] = r.NextDouble();
* }
*
*
*
* double[] R1 = new double[L];
* double[] R2 = new double[L];
* eval.Evaluate(1.0, 1.0, R1);
*
* R2.AccV(1.0, OpAffine);
* OpMatrix.SpMV(1.0, test, 1.0, R2);
*
* Err.AccV(+1.0, R1);
* Err.AccV(-1.0, R2);
*
* double ErrDist = GenericBlas.L2DistPow2(R1, R2).MPISum().Sqrt();
*
* double Ref = test.L2NormPow2().MPISum().Sqrt();
*
* Debug.Assert(ErrDist <= Ref*1.0e-5, "Mismatch between explicit evaluation of XDG operator and matrix.");
* }
*/
}
/// <summary>
/// Calculates the drag (x-component) and lift (y-component) forces acting on a IB contour
/// </summary>
/// <param name="U"></param>
/// <param name="P"></param>
/// <param name="muA"></param>
/// <returns></returns>
static public double[] GetForces(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;
//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>
/// Calculates the drag (x-component) and lift (y-component) forces acting on a cylinder wall of a boundary fitted grid. The definition of the wall is HARDCODED!
/// </summary>
static public double[] GetForces_BoundaryFitted(VectorField <SinglePhaseField> U, SinglePhaseField StressXX, //VectorField<SinglePhaseField> GradU, VectorField<SinglePhaseField> GradV
SinglePhaseField StressXY, SinglePhaseField StressYY, SinglePhaseField P, LevelSetTracker LsTrk, double muA, double beta, string EdgeTagName)
{
int D = LsTrk.GridDat.SpatialDimension;
if (D > 2)
{
throw new ArgumentException("Method GetForces_BoundaryFitted only implemented for 2D (viscoelastic)!");
}
// var UA = U.Select(u => u.GetSpeciesShadowField("A")).ToArray();
var UA = U.ToArray();
//MultidimensionalArray Grad_U = new MultidimensionalArray(D);
//var _GradU = GradU.ToArray();
//var _GradV = GradV.ToArray();
//int RequiredOrder = _GradU[0].Basis.Degree * 3 + 20;
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();
//Console.WriteLine("Forces coeff: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
SinglePhaseField _StressXX = StressXX;
SinglePhaseField _StressXY = StressXY;
SinglePhaseField _StressYY = StressYY;
SinglePhaseField pA = null;
//pA = P.GetSpeciesShadowField("A");
pA = P;
VectorField <SinglePhaseField>[] VelGread = new VectorField <SinglePhaseField> [D];
for (int d = 0; d < D; d++)
{
VelGread[d] = new VectorField <SinglePhaseField>(D, U[d].Basis, (b, name) => new SinglePhaseField(b, name));
VelGread[d].GradientByFlux(1.0, U[d]);
}
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_URes = MultidimensionalArray.Create(Len, K, D);
MultidimensionalArray Grad_VRes = MultidimensionalArray.Create(Len, K, D);
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray StressXXRes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray StressXYRes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray StressYYRes = MultidimensionalArray.Create(Len, K);
var Normals = LsTrk.GridDat.Edges.NormalsCache.GetNormals_Edge(Ns, j0, Len);
//var Normals = MultidimensionalArray.Create(1, Ns.Length, 1);
//var Normals = LsTrk.GridDat.Edges.NormalsForAffine;
for (int i = 0; i < D; i++)
{
VelGread[0][i].EvaluateEdge(j0, Len, Ns, Grad_URes.ExtractSubArrayShallow(-1, -1, i),
Grad_URes.ExtractSubArrayShallow(-1, -1, i), ResultIndexOffset: 0, ResultPreScale: 1);
VelGread[1][i].EvaluateEdge(j0, Len, Ns, Grad_VRes.ExtractSubArrayShallow(-1, -1, i),
Grad_VRes.ExtractSubArrayShallow(-1, -1, i), ResultIndexOffset: 0, ResultPreScale: 1);
//UA[0].EvaluateGradient(j0, Len, Ns, Grad_URes, 0, 1); //
//UA[1].EvaluateGradient(j0, Len, Ns, Grad_VRes, 0, 1); //
//UA[i].EvaluateGradient(j0, Len, Ns, Grad_URes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
//pA.Evaluate(j0, Len, Ns, pARes);
pA.EvaluateEdge(j0, Len, Ns, pARes, pARes, ResultIndexOffset: 0, ResultPreScale: 1);
_StressXX.EvaluateEdge(j0, Len, Ns, StressXXRes, StressXXRes, ResultIndexOffset: 0, ResultPreScale: 1);
_StressXY.EvaluateEdge(j0, Len, Ns, StressXYRes, StressXYRes, ResultIndexOffset: 0, ResultPreScale: 1);
_StressYY.EvaluateEdge(j0, Len, Ns, StressYYRes, StressYYRes, ResultIndexOffset: 0, ResultPreScale: 1);
//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) * beta) * Grad_URes[j, k, 0] * Normals[j, k, 0];
acc -= ((muA) * beta) * Grad_URes[j, k, 1] * Normals[j, k, 1];
acc -= ((muA) * beta) * Grad_VRes[j, k, 0] * Normals[j, k, 1];
acc -= (muA) * StressXXRes[j, k] * Normals[j, k, 0];
acc -= (muA) * StressXYRes[j, k] * Normals[j, k, 1];
break;
case 1:
acc += pARes[j, k] * Normals[j, k, 1];
acc -= (2 * (muA) * beta) * Grad_VRes[j, k, 1] * Normals[j, k, 1];
acc -= ((muA) * beta) * Grad_VRes[j, k, 0] * Normals[j, k, 0];
acc -= ((muA) * beta) * Grad_URes[j, k, 1] * Normals[j, k, 0];
acc -= (muA) * StressXYRes[j, k] * Normals[j, k, 0];
acc -= (muA) * StressYYRes[j, k] * Normals[j, k, 1];
break;
default:
throw new NotImplementedException();
}
result[j, k] = acc;
}
}
};
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
//EdgeMask Mask = new EdgeMask(LsTrk.GridDat, "Wall_bottom");
EdgeMask Mask = new EdgeMask(LsTrk.GridDat, EdgeTagName);
EdgeQuadratureScheme eqs = SchemeHelper.GetEdgeQuadScheme(LsTrk.GetSpeciesId("A"), IntegrationDomain: Mask);
EdgeQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
eqs.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);
}
public XDGTestSetup(
int p,
double AggregationThreshold,
int TrackerWidth,
MultigridOperator.Mode mumo,
XQuadFactoryHelper.MomentFittingVariants momentFittingVariant,
ScalarFunction LevSetFunc = null)
{
// Level set, tracker and XDG basis
// ================================
if (LevSetFunc == null)
{
LevSetFunc = ((_2D)((x, y) => 0.8 * 0.8 - x * x - y * y)).Vectorize();
}
LevSet = new LevelSet(new Basis(grid, 2), "LevelSet");
LevSet.Clear();
LevSet.ProjectField(LevSetFunc);
LsTrk = new LevelSetTracker(grid, XQuadFactoryHelper.MomentFittingVariants.Classic, TrackerWidth, new string[] { "A", "B" }, LevSet);
LsTrk.UpdateTracker();
XB = new XDGBasis(LsTrk, p);
XSpatialOperator Dummy = new XSpatialOperator(1, 0, 1, QuadOrderFunc.SumOfMaxDegrees(RoundUp: true), "C1", "u");
//Dummy.EquationComponents["c1"].Add(new
Dummy.Commit();
//Tecplot.PlotFields(new DGField[] { LevSet }, "agglo", 0.0, 3);
// operator
// ========
Debug.Assert(p <= 4);
XDGBasis opXB = new XDGBasis(LsTrk, 4); // we want to have a very precise quad rule
var map = new UnsetteledCoordinateMapping(opXB);
int quadOrder = Dummy.QuadOrderFunction(map.BasisS.Select(bs => bs.Degree).ToArray(), new int[0], map.BasisS.Select(bs => bs.Degree).ToArray());
//agg = new MultiphaseCellAgglomerator(new CutCellMetrics(momentFittingVariant, quadOrder, LsTrk, LsTrk.SpeciesIdS.ToArray()), AggregationThreshold, false);
agg = LsTrk.GetAgglomerator(LsTrk.SpeciesIdS.ToArray(), quadOrder, __AgglomerationTreshold: AggregationThreshold);
foreach (var S in LsTrk.SpeciesIdS)
{
Console.WriteLine("Species {0}, no. of agglomerated cells {1} ",
LsTrk.GetSpeciesName(S),
agg.GetAgglomerator(S).AggInfo.SourceCells.Count());
}
// mass matrix factory
// ===================
// Basis maxB = map.BasisS.ElementAtMax(b => b.Degree);
//MassFact = new MassMatrixFactory(maxB, agg);
MassFact = LsTrk.GetXDGSpaceMetrics(LsTrk.SpeciesIdS.ToArray(), quadOrder, 1).MassMatrixFactory;
// Test field
// ==========
// set the test field: this is a polynomial function,
// but different for each species; On this field, restriction followed by prolongation should be the identity
this.uTest = new XDGField(this.XB, "uTest");
Dictionary <SpeciesId, double> dumia = new Dictionary <SpeciesId, double>();
int i = 2;
foreach (var Spc in LsTrk.SpeciesIdS)
{
dumia.Add(Spc, i);
i -= 1;
}
SetTestValue(uTest, dumia);
// dummy operator matrix which fits polynomial degree p
// ====================================================
opMtx = new BlockMsrMatrix(uTest.Mapping, uTest.Mapping);
opMtx.AccEyeSp(120.0);
// XDG Aggregation BasiseS
// =======================
XAggB = MgSeq.Select(agGrd => new XdgAggregationBasis[] { new XdgAggregationBasis(uTest.Basis, agGrd) }).ToArray();
for (int iLevel = 0; iLevel < XAggB.Length; iLevel++)
{
var xab = XAggB[iLevel];
Debug.Assert(xab.Length == 1);
xab[0].Update(agg);
}
// Multigrid Operator
// ==================
opMtx = new BlockMsrMatrix(uTest.Mapping, uTest.Mapping);
opMtx.AccEyeSp(120.0);
MultigridOp = new MultigridOperator(XAggB, uTest.Mapping,
opMtx,
MassFact.GetMassMatrix(uTest.Mapping, false),
new MultigridOperator.ChangeOfBasisConfig[][] {
new MultigridOperator.ChangeOfBasisConfig[] {
new MultigridOperator.ChangeOfBasisConfig()
{
VarIndex = new int[] { 0 }, mode = mumo, Degree = p
}
}
});
}
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>
/// 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>
public void AssembleMatrix_Timestepper <T>(
int CutCellQuadOrder,
BlockMsrMatrix OpMatrix, double[] OpAffine,
Dictionary <SpeciesId, MultidimensionalArray> AgglomeratedCellLengthScales,
IEnumerable <T> U0,
VectorField <SinglePhaseField> SurfaceForce,
VectorField <SinglePhaseField> LevelSetGradient, SinglePhaseField ExternalyProvidedCurvature,
UnsetteledCoordinateMapping RowMapping, UnsetteledCoordinateMapping ColMapping,
double time) where T : DGField
{
if (ColMapping.BasisS.Count != this.Op.DomainVar.Count)
{
throw new ArgumentException();
}
if (RowMapping.BasisS.Count != this.Op.CodomainVar.Count)
{
throw new ArgumentException();
}
// check:
var Tracker = this.LsTrk;
int D = Tracker.GridDat.SpatialDimension;
if (U0 != null && U0.Count() != D)
{
throw new ArgumentException();
}
LevelSet Phi = (LevelSet)(Tracker.LevelSets[0]);
SpeciesId[] SpcToCompute = AgglomeratedCellLengthScales.Keys.ToArray();
// parameter assembly
// ==================
// normals:
SinglePhaseField[] Normals; // Normal vectors: length not normalized - will be normalized at each quad node within the flux functions.
if (this.NormalsRequired)
{
if (LevelSetGradient == null)
{
LevelSetGradient = new VectorField <SinglePhaseField>(D, Phi.Basis, SinglePhaseField.Factory);
LevelSetGradient.Gradient(1.0, Phi);
}
Normals = LevelSetGradient.ToArray();
}
else
{
Normals = new SinglePhaseField[D];
}
// curvature:
SinglePhaseField Curvature;
if (this.CurvatureRequired)
{
Curvature = ExternalyProvidedCurvature;
}
else
{
Curvature = null;
}
// linearization velocity:
DGField[] U0_U0mean;
if (this.U0meanrequired)
{
XDGBasis U0meanBasis = new XDGBasis(Tracker, 0);
VectorField <XDGField> U0mean = new VectorField <XDGField>(D, U0meanBasis, "U0mean_", XDGField.Factory);
U0_U0mean = ArrayTools.Cat <DGField>(U0, U0mean);
}
else
{
U0_U0mean = new DGField[2 * D];
}
// concatenate everything
var Params = ArrayTools.Cat <DGField>(
U0_U0mean,
Curvature,
((SurfaceForce != null) ? SurfaceForce.ToArray() : new SinglePhaseField[D]),
Normals);
// linearization velocity:
if (this.U0meanrequired)
{
VectorField <XDGField> U0mean = new VectorField <XDGField>(U0_U0mean.Skip(D).Take(D).Select(f => ((XDGField)f)).ToArray());
U0mean.Clear();
if (this.physParams.IncludeConvection)
{
ComputeAverageU(U0, U0mean, CutCellQuadOrder, LsTrk.GetXDGSpaceMetrics(SpcToCompute, CutCellQuadOrder, 1).XQuadSchemeHelper);
}
}
// assemble the matrix & affine vector
// ===================================
// compute matrix
Op.ComputeMatrixEx(Tracker,
ColMapping, Params, RowMapping,
OpMatrix, OpAffine, false, time, true,
AgglomeratedCellLengthScales,
SpcToCompute);
}
/// <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]);
}
}