/// <summary>
/// Computes the maximum admissible step-size according to
/// GassnerEtAl2008, equation 67.
/// </summary>
/// <param name="i0"></param>
/// <param name="Length"></param>
/// <returns></returns>
protected override double GetCFLStepSize(int i0, int Length)
{
int iKref = gridData.Cells.GetRefElementIndex(i0);
int noOfNodesPerCell = base.EvaluationPoints[iKref].NoOfNodes;
MultidimensionalArray levelSetValues =
speciesMap.Tracker.DataHistories[0].Current.GetLevSetValues(base.EvaluationPoints[iKref], i0, Length);
SpeciesId species = speciesMap.Tracker.GetSpeciesId(speciesMap.Control.FluidSpeciesName);
var hMinArray = speciesMap.CellAgglomeration.CellLengthScales[species];
//var volFrac = speciesMap.QuadSchemeHelper.CellAgglomeration.CellVolumeFrac[species];
//var hMinGass = speciesMap.h_min;
//var hMin = gridData.Cells.h_min;
double cfl = double.MaxValue;
for (int i = 0; i < Length; i++)
{
int cell = i0 + i;
//double hmin = hMin[cell] * volFrac[cell];
double hmin = hMinArray[cell];
//double hmin = hMinGass[cell];
for (int node = 0; node < noOfNodesPerCell; node++)
{
if (levelSetValues[i, node].Sign() != (double)speciesMap.Control.FluidSpeciesSign)
{
continue;
}
Material material = speciesMap.GetMaterial(double.NaN);
Vector3D momentum = new Vector3D();
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
momentum[d] = momentumValues[d][i, node];
}
StateVector state = new StateVector(
material, densityValues[i, node], momentum, energyValues[i, node]);
double coeff = Math.Max(4.0 / 3.0, config.EquationOfState.HeatCapacityRatio / config.PrandtlNumber);
double cflhere = hmin * hmin / coeff / (state.GetViscosity(cell) / config.ReynoldsNumber);
#if DEBUG
if (double.IsNaN(cflhere))
{
throw new Exception("Could not determine CFL number");
}
#endif
cfl = Math.Min(cfl, cflhere);
}
}
int degree = workingSet.ConservativeVariables.Max(f => f.Basis.Degree);
int twoNPlusOne = 2 * degree + 1;
return(cfl * GetBetaMax(degree) / twoNPlusOne / twoNPlusOne / Math.Sqrt(CNSEnvironment.NumberOfDimensions));
//return cfl / twoNPlusOne / twoNPlusOne;
}
/// <summary>
/// Computes the maximum admissible step-size according to
/// GassnerEtAl2008, equation 67.
/// </summary>
/// <param name="i0"></param>
/// <param name="Length"></param>
/// <returns></returns>
protected override double GetCFLStepSize(int i0, int Length)
{
int iKref = gridData.Cells.GetRefElementIndex(i0);
int noOfNodesPerCell = base.EvaluationPoints[iKref].NoOfNodes;
Material material = speciesMap.GetMaterial(double.NaN);
var hmin = gridData.Cells.h_min;
double scaling = Math.Max(4.0 / 3.0, config.EquationOfState.HeatCapacityRatio / config.PrandtlNumber);
// Following code is performance-critical, so expect spagetti code ahead
double cfl = double.MaxValue;
switch (speciesMap)
{
// 1) IBM optimized (ignores nodes in the void part of a cell, only applies to constant viscosity gases)
case ImmersedSpeciesMap ibmMap when material.ViscosityLaw is ConstantViscosity: {
MultidimensionalArray levelSetValues =
ibmMap.Tracker.DataHistories[0].Current.GetLevSetValues(base.EvaluationPoints[iKref], i0, Length);
SpeciesId species = ibmMap.Tracker.GetSpeciesId(ibmMap.Control.FluidSpeciesName);
//var hMin = speciesMap.QuadSchemeHelper.CellAgglomeration.CellLengthScales[species];
var volFrac = ibmMap.CellAgglomeration.CellVolumeFrac[species];
double nu = 1.0 / config.ReynoldsNumber;
for (int i = 0; i < Length; i++)
{
int cell = i0 + i;
double hminlocal = hmin[cell] * volFrac[cell];
//double hminlocal = hMin[cell];
//double hmin = hMinGass[cell];
for (int node = 0; node < noOfNodesPerCell; node++)
{
if (levelSetValues[i, node].Sign() != (double)ibmMap.Control.FluidSpeciesSign)
{
continue;
}
double cflhere = hminlocal * hminlocal / scaling / nu;
#if DEBUG
if (double.IsNaN(cflhere))
{
throw new Exception("Could not determine CFL number");
}
#endif
cfl = Math.Min(cfl, cflhere);
}
}
}
break;
// 2) IBM generic (ignores nodes in the void part of a cell)
case ImmersedSpeciesMap ibmMap: {
MultidimensionalArray levelSetValues =
ibmMap.Tracker.DataHistories[0].Current.GetLevSetValues(base.EvaluationPoints[iKref], i0, Length);
SpeciesId species = ibmMap.Tracker.GetSpeciesId(ibmMap.Control.FluidSpeciesName);
//var hMin = speciesMap.QuadSchemeHelper.CellAgglomeration.CellLengthScales[species];
var volFrac = ibmMap.CellAgglomeration.CellVolumeFrac[species];
for (int i = 0; i < Length; i++)
{
int cell = i0 + i;
double hminlocal = hmin[cell] * volFrac[cell];
//double hminlocal = hMin[cell];
//double hmin = hMinGass[cell];
for (int node = 0; node < noOfNodesPerCell; node++)
{
if (levelSetValues[i, node].Sign() != (double)ibmMap.Control.FluidSpeciesSign)
{
continue;
}
Vector3D momentum = new Vector3D();
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
momentum[d] = momentumValues[d][i, node];
}
StateVector state = new StateVector(
material, densityValues[i, node], momentum, energyValues[i, node]);
double nu = state.GetViscosity(cell) / config.ReynoldsNumber;
Debug.Assert(nu > 0.0);
double cflhere = hminlocal * hminlocal / scaling / nu;
#if DEBUG
if (double.IsNaN(cflhere))
{
throw new Exception("Could not determine CFL number");
}
#endif
cfl = Math.Min(cfl, cflhere);
}
}
}
break;
// 3) Non-IBM optimized (only applies to constant viscosity gases)
case var speciesMap when material.ViscosityLaw is ConstantViscosity: {
double nu = 1.0 / config.ReynoldsNumber; // Constant viscosity
for (int i = 0; i < Length; i++)
{
int cell = i0 + i;
for (int node = 0; node < noOfNodesPerCell; node++)
{
double hminlocal = gridData.Cells.h_min[cell];
double cflhere = hminlocal * hminlocal / scaling / nu;
cfl = Math.Min(cfl, cflhere);
}
}
}
break;
// 4) Non-IBM generic (works for all viscosity laws)
default: {
for (int i = 0; i < Length; i++)
{
int cell = i0 + i;
for (int node = 0; node < noOfNodesPerCell; node++)
{
Vector3D momentum = new Vector3D();
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
momentum[d] = momentumValues[d][i, node];
}
StateVector state = new StateVector(
material, densityValues[i, node], momentum, energyValues[i, node]);
double hminlocal = hmin[cell];
double nu = state.GetViscosity(cell) / config.ReynoldsNumber;
Debug.Assert(nu > 0.0);
double cflhere = hminlocal * hminlocal / scaling / nu;
cfl = Math.Min(cfl, cflhere);
}
}
}
break;
}
int degree = workingSet.ConservativeVariables.Max(f => f.Basis.Degree);
int twoNPlusOne = 2 * degree + 1;
return(cfl * GetBetaMax(degree) / twoNPlusOne / twoNPlusOne / Math.Sqrt(CNSEnvironment.NumberOfDimensions));
}
/// <summary>
/// <see cref="SIPGFlux.UpdateTensorComponent(StateVector, bool, double[,,], int)"/>
/// </summary>
/// <param name="state"></param>
/// <param name="adiabaticWall"></param>
/// <param name="Tensor"></param>
/// <param name="cellIndex"></param>
protected override void UpdateTensorComponent(StateVector state, bool adiabaticWall, double[, ,] Tensor, int cellIndex)
{
double Viscosity = state.GetViscosity(cellIndex);
double gamma = config.EquationOfState.HeatCapacityRatio;
double gamma_Pr = adiabaticWall ? 0 :
gamma / config.PrandtlNumber;
double mu_rhoRe = Viscosity / config.ReynoldsNumber / state.Density;
double MachsScaling = gamma * config.MachNumber * config.MachNumber;
double v1 = state.Momentum[0] / state.Density;
double v2 = state.Momentum[1] / state.Density;
double v3 = state.Momentum[2] / state.Density;
double E = state.Energy / state.Density;
double VelocitySquared = v1 * v1 + v2 * v2 + v3 * v3;
switch (dimension)
{
case 1:
Tensor[0, 0, 0] = -(MachsScaling * (alphaPlus13 * v1 * v1 + VelocitySquared) + gamma_Pr * (E - MachsScaling * VelocitySquared)) * mu_rhoRe;
Tensor[0, 0, 1] = MachsScaling * (alphaPlus43 - gamma_Pr) * v1 * mu_rhoRe;
Tensor[0, 0, 2] = gamma_Pr * mu_rhoRe;
break;
case 2:
// G_xx
Tensor[0, 0, 0] = -(MachsScaling * (alphaPlus13 * v1 * v1 + VelocitySquared) + gamma_Pr * (E - MachsScaling * VelocitySquared)) * mu_rhoRe;
Tensor[0, 0, 1] = MachsScaling * (alphaPlus43 - gamma_Pr) * v1 * mu_rhoRe;
Tensor[0, 0, 2] = MachsScaling * (1 - gamma_Pr) * v2 * mu_rhoRe;
Tensor[0, 0, 3] = gamma_Pr * mu_rhoRe;
// G_xy
Tensor[0, 1, 0] = -MachsScaling * alphaPlus13 * v1 * v2 * mu_rhoRe;
Tensor[0, 1, 1] = MachsScaling * v2 * mu_rhoRe;
Tensor[0, 1, 2] = MachsScaling * alphaMinus23 * v1 * mu_rhoRe;
//Tensor[0, 1, 3] = 0*eta_rhoRe;
// G_yx
Tensor[1, 0, 0] = -MachsScaling * (alphaPlus43 - 1.0) * v1 * v2 * mu_rhoRe;
Tensor[1, 0, 1] = MachsScaling * alphaMinus23 * v2 * mu_rhoRe;
Tensor[1, 0, 2] = MachsScaling * v1 * mu_rhoRe;
//Tensor[1, 0, 3] = 0*eta_rhoRe;
// G_yy
Tensor[1, 1, 0] = -(MachsScaling * (alphaPlus13 * v2 * v2 + VelocitySquared) + gamma_Pr * (E - MachsScaling * VelocitySquared)) * mu_rhoRe;
Tensor[1, 1, 1] = MachsScaling * (1 - gamma_Pr) * v1 * mu_rhoRe;
Tensor[1, 1, 2] = MachsScaling * (alphaPlus43 - gamma_Pr) * v2 * mu_rhoRe;
Tensor[1, 1, 3] = gamma_Pr * mu_rhoRe;
break;
case 3:
// G_xx
Tensor[0, 0, 0] = -(MachsScaling * (alphaPlus13 * v1 * v1 + VelocitySquared) + gamma_Pr * (E - MachsScaling * VelocitySquared)) * mu_rhoRe;
Tensor[0, 0, 1] = MachsScaling * (alphaPlus43 - gamma_Pr) * v1 * mu_rhoRe;
Tensor[0, 0, 2] = MachsScaling * (1 - gamma_Pr) * v2 * mu_rhoRe;
Tensor[0, 0, 3] = MachsScaling * (1 - gamma_Pr) * v3 * mu_rhoRe;
Tensor[0, 0, 4] = gamma_Pr * mu_rhoRe;
// G_xy
Tensor[0, 1, 0] = -MachsScaling * alphaPlus13 * v1 * v2 * mu_rhoRe;
Tensor[0, 1, 1] = MachsScaling * v2 * mu_rhoRe;
Tensor[0, 1, 2] = MachsScaling * alphaMinus23 * v1 * mu_rhoRe;
//Tensor[0, 1, 3] = 0 * eta_rhoRe;
//Tensor[0, 1, 4] = 0 * eta_rhoRe;
// G_xz
Tensor[0, 2, 0] = -MachsScaling * alphaPlus13 * v1 * v3 * mu_rhoRe;
Tensor[0, 2, 1] = MachsScaling * v3 * mu_rhoRe;
//Tensor[0, 2, 2] = 0 * eta_rhoRe;
Tensor[0, 2, 3] = MachsScaling * alphaMinus23 * v1 * mu_rhoRe;
//Tensor[0, 2, 4] = 0 * eta_rhoRe;
// G_yx
Tensor[1, 0, 0] = -MachsScaling * alphaPlus13 * v1 * v2 * mu_rhoRe;
Tensor[1, 0, 1] = MachsScaling * alphaMinus23 * v2 * mu_rhoRe;
Tensor[1, 0, 2] = MachsScaling * v1 * mu_rhoRe;
//Tensor[1, 0, 3] = 0 * eta_rhoRe;
//Tensor[1, 0, 4] = 0 * eta_rhoRe;
// G_yy
Tensor[1, 1, 0] = -(MachsScaling * (alphaPlus13 * v2 * v2 + VelocitySquared) + gamma_Pr * (E - MachsScaling * VelocitySquared)) * mu_rhoRe;
Tensor[1, 1, 1] = MachsScaling * (1 - gamma_Pr) * v1 * mu_rhoRe;
Tensor[1, 1, 2] = MachsScaling * (alphaPlus43 - gamma_Pr) * v2 * mu_rhoRe;
Tensor[1, 1, 3] = MachsScaling * (1 - gamma_Pr) * v3 * mu_rhoRe;
Tensor[1, 1, 4] = gamma_Pr * mu_rhoRe;
// G_yz
Tensor[1, 2, 0] = -MachsScaling * alphaPlus13 * v2 * v3 * mu_rhoRe;
//Tensor[1, 2, 1] = 0 * eta_rhoRe;
Tensor[1, 2, 2] = MachsScaling * v3 * mu_rhoRe;
Tensor[1, 2, 3] = MachsScaling * alphaMinus23 * v2 * mu_rhoRe;
//Tensor[1, 2, 4] = 0 * eta_rhoRe;
// G_zx
Tensor[2, 0, 0] = -MachsScaling * alphaPlus13 * v1 * v3 * mu_rhoRe;
Tensor[2, 0, 1] = MachsScaling * alphaMinus23 * v3 * mu_rhoRe;
//Tensor[2, 0, 2] = 0 * eta_rhoRe;
Tensor[2, 0, 3] = MachsScaling * v1 * mu_rhoRe;
//Tensor[2, 0, 4] = 0 * eta_rhoRe;
// G_zy
Tensor[2, 1, 0] = -MachsScaling * alphaPlus13 * v2 * v3 * mu_rhoRe;
//Tensor[2, 1, 1] = 0 * eta_rhoRe;
Tensor[2, 1, 2] = MachsScaling * alphaMinus23 * v3 * mu_rhoRe;
Tensor[2, 1, 3] = MachsScaling * v2 * mu_rhoRe;
//Tensor[2, 1, 4] = 0 * eta_rhoRe;
// G_zz
Tensor[2, 2, 0] = -(MachsScaling * (alphaPlus13 * v3 * v3 + VelocitySquared) + gamma_Pr * (E - MachsScaling * VelocitySquared)) * mu_rhoRe;
Tensor[2, 2, 1] = MachsScaling * (1 - gamma_Pr) * v1 * mu_rhoRe;
Tensor[2, 2, 2] = MachsScaling * (1 - gamma_Pr) * v2 * mu_rhoRe;
Tensor[2, 2, 3] = MachsScaling * (alphaPlus43 - gamma_Pr) * v3 * mu_rhoRe;
Tensor[2, 2, 4] = gamma_Pr * mu_rhoRe;
break;
}
}
/// <summary>
/// <see cref="SIPGFlux.UpdateTensorComponent(StateVector, bool, double[,,], int)"/>
/// </summary>
/// <param name="state"></param>
/// <param name="adiabaticWall"></param>
/// <param name="Tensor"></param>
/// <param name="cellIndex"></param>
protected override void UpdateTensorComponent(StateVector state, bool adiabaticWall, double[, ,] Tensor, int cellIndex)
{
//TO-DO: temperature dependent thermal conductivity/viscosity
// double ThermalConductivity = state.ThermalConductivity
double Viscosity = state.GetViscosity(cellIndex);
double ThermalConductivity = Viscosity;
double mu_rhoRe = Viscosity / config.ReynoldsNumber / state.Density;
double v1 = state.Velocity[0];
double v2 = state.Velocity[1];
double v3 = state.Velocity[2];
switch (dimension)
{
case 1:
Tensor[0, 0, 0] = -(alphaPlus43) * v1 * mu_rhoRe;
Tensor[0, 0, 1] = alphaPlus43 * mu_rhoRe;
//Tensor[0, 0, 2] = 0 * eta_rhoRe;
break;
case 2:
switch (component)
{
case 1: // x-momentum
//G_xx
Tensor[0, 0, 0] = -(alphaPlus43) * v1 * mu_rhoRe;
Tensor[0, 0, 1] = alphaPlus43 * mu_rhoRe;
//Tensor[0, 0, 2] = 0 * eta_rhoRe;
//Tensor[0, 0, 3] = 0 * eta_rhoRe;
//G_xy
Tensor[0, 1, 0] = -alphaMinus23 * v2 * mu_rhoRe;
//Tensor[0, 1, 1] = 0 * eta_rhoRe;
Tensor[0, 1, 2] = alphaMinus23 * mu_rhoRe;
//Tensor[0, 1, 3] = 0 * eta_rhoRe;
// G_yx
Tensor[1, 0, 0] = -v2 * mu_rhoRe;
//Tensor[1, 0, 1] = 0 * eta_rhoRe;
Tensor[1, 0, 2] = 1 * mu_rhoRe;
//Tensor[1, 0, 3] = 0 * eta_rhoRe;
//G_yy
Tensor[1, 1, 0] = -v1 * mu_rhoRe;
Tensor[1, 1, 1] = 1 * mu_rhoRe;
//Tensor[1, 1, 2] = 0 * eta_rhoRe;
//Tensor[1, 1, 3] = 0 * eta_rhoRe;
break;
case 2: // y-momentum
//G_xx
Tensor[0, 0, 0] = -v2 * mu_rhoRe;
//Tensor[0, 0, 1] = 0 * eta_rhoRe;
Tensor[0, 0, 2] = 1 * mu_rhoRe;
//Tensor[0, 0, 3] = 0 * eta_rhoRe;
//G_xy
Tensor[0, 1, 0] = -v2 * mu_rhoRe;
Tensor[0, 1, 1] = 1 * mu_rhoRe;
//Tensor[0, 1, 2] = 0 * eta_rhoRe;
//Tensor[0, 1, 3] = 0 * eta_rhoRe;
// G_yx
Tensor[1, 0, 0] = -alphaMinus23 * v1 * mu_rhoRe;
Tensor[1, 0, 1] = alphaMinus23 * mu_rhoRe;
//Tensor[1, 0, 2] = 0 * eta_rhoRe;
//Tensor[1, 0, 3] = 0 * eta_rhoRe;
//G_yy
Tensor[1, 1, 0] = -(alphaPlus43) * v2 * mu_rhoRe;
//Tensor[1, 1, 1] = 0 * eta_rhoRe;
Tensor[1, 1, 2] = alphaPlus43 * mu_rhoRe;
//Tensor[1, 1, 3] = 0 * eta_rhoRe;
break;
}
break;
case 3:
switch (component)
{
case 1: // x-momentum
//G_xx
Tensor[0, 0, 0] = -alphaPlus43 * v1 * mu_rhoRe;
Tensor[0, 0, 1] = alphaPlus43 * mu_rhoRe;
//Tensor[0, 0, 2] = 0 * eta_rhoRe;
//Tensor[0, 0, 3] = 0 * eta_rhoRe;
//Tensor[0, 0, 4] = 0 * eta_rhoRe;
//G_xy
Tensor[0, 1, 0] = -alphaMinus23 * v2 * mu_rhoRe;
//Tensor[0, 1, 1] = 0 * eta_rhoRe;
Tensor[0, 1, 2] = alphaMinus23 * mu_rhoRe;
//Tensor[0, 1, 3] = 0 * eta_rhoRe;
//Tensor[0, 1, 4] = 0 * eta_rhoRe;
//G_xz
Tensor[0, 2, 0] = -alphaMinus23 * v3 * mu_rhoRe;
//Tensor[0, 2, 1] = 0 * eta_rhoRe;
//Tensor[0, 2, 2] = 0 * eta_rhoRe;
Tensor[0, 2, 3] = alphaMinus23 * mu_rhoRe;
//Tensor[0, 2, 4] = 0 * eta_rhoRe;
// G_yx
Tensor[1, 0, 0] = -v2 * mu_rhoRe;
//Tensor[1, 0, 1] = 0 * eta_rhoRe;
Tensor[1, 0, 2] = 1 * mu_rhoRe;
//Tensor[1, 0, 3] = 0 * eta_rhoRe;
//Tensor[1, 0, 4] = 0 * eta_rhoRe;
//G_yy
Tensor[1, 1, 0] = -v1 * mu_rhoRe;
Tensor[1, 1, 1] = 1 * mu_rhoRe;
//Tensor[1, 1, 2] = 0 * eta_rhoRe;
//Tensor[1, 1, 3] = 0 * eta_rhoRe;
//Tensor[1, 1, 4] = 0 * eta_rhoRe;
//G_yz
//Tensor[1, 2, 0] = 0 * eta_rhoRe;
//Tensor[1, 2, 1] = 0 * eta_rhoRe;
//Tensor[1, 2, 2] = 0 * eta_rhoRe;
//Tensor[1, 2, 3] = 0 * eta_rhoRe;
//Tensor[1, 2, 4] = 0 * eta_rhoRe;
// G_zx
Tensor[2, 0, 0] = -v3 * mu_rhoRe;
//Tensor[2, 0, 1] = 0 * eta_rhoRe;
//Tensor[2, 0, 2] = 0 * eta_rhoRe;
Tensor[2, 0, 3] = 1 * mu_rhoRe;
//Tensor[2, 0, 4] = 0 * eta_rhoRe;
//G_zy
//Tensor[2, 1, 0] = 0 * eta_rhoRe;
//Tensor[2, 1, 1] = 0 * eta_rhoRe;
//Tensor[2, 1, 2] = 0 * eta_rhoRe;
//Tensor[2, 1, 3] = 0 * eta_rhoRe;
//Tensor[2, 1, 4] = 0 * eta_rhoRe;
//G_zz
Tensor[2, 2, 0] = -v1 * mu_rhoRe;
Tensor[2, 2, 1] = 1 * mu_rhoRe;
//Tensor[2, 2, 2] = 0 * eta_rhoRe;
//Tensor[2, 2, 3] = 0 * eta_rhoRe;
//Tensor[2, 2, 4] = 0 * eta_rhoRe;
break;
case 2: // y-momentum
//G_xx
Tensor[0, 0, 0] = -v2 * mu_rhoRe;
//Tensor[0, 0, 1] = 0 * eta_rhoRe;
Tensor[0, 0, 2] = 1 * mu_rhoRe;
//Tensor[0, 0, 3] = 0 * eta_rhoRe;
//Tensor[0, 0, 4] = 0 * eta_rhoRe;
//G_xy
Tensor[0, 1, 0] = -v1 * mu_rhoRe;
Tensor[0, 1, 1] = 1 * mu_rhoRe;
//Tensor[0, 1, 2] = 0 * eta_rhoRe;
//Tensor[0, 1, 3] = 0 * eta_rhoRe;
//Tensor[0, 1, 4] = 0 * eta_rhoRe;
//G_xz
//Tensor[0, 2, 0] = 0 * eta_rhoRe;
//Tensor[0, 2, 1] = 0 * eta_rhoRe;
//Tensor[0, 2, 2] = 0 * eta_rhoRe;
//Tensor[0, 2, 3] = 0 * eta_rhoRe;
//Tensor[0, 2, 4] = 0 * eta_rhoRe;
// G_yx
Tensor[1, 0, 0] = -alphaMinus23 * v1 * mu_rhoRe;
Tensor[1, 0, 1] = alphaMinus23 * mu_rhoRe;
//Tensor[1, 0, 2] = 0 * eta_rhoRe;
//Tensor[1, 0, 3] = 0 * eta_rhoRe;
//Tensor[1, 0, 4] = 0 * eta_rhoRe;
//G_yy
Tensor[1, 1, 0] = -alphaPlus43 * v2 * mu_rhoRe;
//Tensor[1, 1, 1] = 0 * eta_rhoRe;
Tensor[1, 1, 2] = alphaPlus43 * mu_rhoRe;
//Tensor[1, 1, 3] = 0 * eta_rhoRe;
//Tensor[1, 1, 4] = 0 * eta_rhoRe;
// G_yz
Tensor[1, 2, 0] = -alphaMinus23 * v3 * mu_rhoRe;
//Tensor[1, 2, 1] = 0 * eta_rhoRe;
//Tensor[1, 2, 2] = 0 * eta_rhoRe;
Tensor[1, 2, 3] = alphaMinus23 * mu_rhoRe;
//Tensor[1, 2, 4] = 0 * eta_rhoRe;
//G_zx
//Tensor[2, 0, 0] = 0 * eta_rhoRe;
//Tensor[2, 0, 1] = 0 * eta_rhoRe;
//Tensor[2, 0, 2] = 0 * eta_rhoRe;
//Tensor[2, 0, 3] = 0 * eta_rhoRe;
//Tensor[2, 0, 4] = 0 * eta_rhoRe;
//G_zy
Tensor[2, 1, 0] = -v3 * mu_rhoRe;
//Tensor[2, 1, 1] = 0 * eta_rhoRe;
//Tensor[2, 1, 2] = 0 * eta_rhoRe;
Tensor[2, 1, 3] = 1 * mu_rhoRe;
//Tensor[2, 1, 4] = 0 * eta_rhoRe;
//G_zz
Tensor[2, 2, 0] = -v2 * mu_rhoRe;
//Tensor[2, 2, 1] = 0 * eta_rhoRe;
Tensor[2, 2, 2] = 1 * mu_rhoRe;
//Tensor[2, 2, 3] = 0 * eta_rhoRe;
//Tensor[2, 2, 4] = 0 * eta_rhoRe;
break;
case 3: // z-momentum
//G_xx
Tensor[0, 0, 0] = -v3 * mu_rhoRe;
//Tensor[0, 0, 1] = 0 * eta_rhoRe;
//Tensor[0, 0, 2] = 0 * eta_rhoRe;
Tensor[0, 0, 3] = 1 * mu_rhoRe;
//Tensor[0, 0, 4] = 0 * eta_rhoRe;
//G_xy
//Tensor[0, 1, 0] = 0 * eta_rhoRe;
//Tensor[0, 1, 1] = 0 * eta_rhoRe;
//Tensor[0, 1, 2] = 0 * eta_rhoRe;
//Tensor[0, 1, 3] = 0 * eta_rhoRe;
//Tensor[0, 1, 4] = 0 * eta_rhoRe;
//G_xz
Tensor[0, 2, 0] = -v1 * mu_rhoRe;
Tensor[0, 2, 1] = 1 * mu_rhoRe;
//Tensor[0, 2, 2] = 0 * eta_rhoRe;
//Tensor[0, 2, 3] = 0 * eta_rhoRe;
//Tensor[0, 2, 4] = 0 * eta_rhoRe;
// G_yx
//Tensor[1, 0, 0] = 0 * eta_rhoRe;
//Tensor[1, 0, 1] = 0 * eta_rhoRe;
//Tensor[1, 0, 2] = 0 * eta_rhoRe;
//Tensor[1, 0, 3] = 0 * eta_rhoRe;
//Tensor[1, 0, 4] = 0 * eta_rhoRe;
//G_yy
Tensor[1, 1, 0] = -v3 * mu_rhoRe;
//Tensor[1, 1, 1] = 0 * eta_rhoRe;
//Tensor[1, 1, 2] = 0 * eta_rhoRe;
Tensor[1, 1, 3] = 1 * mu_rhoRe;
//Tensor[1, 1, 4] = 0 * eta_rhoRe;
// G_yz
Tensor[1, 2, 0] = -v2 * mu_rhoRe;
//Tensor[1, 2, 1] = 0 * eta_rhoRe;
Tensor[1, 2, 2] = 1 * mu_rhoRe;
//Tensor[1, 2, 3] = 0 * eta_rhoRe;
//Tensor[1, 2, 4] = 0 * eta_rhoRe;
//G_zx
Tensor[2, 0, 0] = -alphaMinus23 * v1 * mu_rhoRe;
Tensor[2, 0, 1] = alphaMinus23 * mu_rhoRe;
//Tensor[2, 0, 2] = 0 * eta_rhoRe;
//Tensor[2, 0, 3] = 0 * eta_rhoRe;
//Tensor[2, 0, 4] = 0 * eta_rhoRe;
//G_zy
Tensor[2, 1, 0] = -alphaMinus23 * v2 * mu_rhoRe;
//Tensor[2, 1, 1] = 0 * eta_rhoRe;
Tensor[2, 1, 2] = alphaMinus23 * mu_rhoRe;
//Tensor[2, 1, 3] = 0 * eta_rhoRe;
//Tensor[2, 1, 4] = 0 * eta_rhoRe;
//G_zz
Tensor[2, 2, 0] = -alphaPlus43 * v3 * mu_rhoRe;
//Tensor[2, 2, 1] = 0 * eta_rhoRe;
//Tensor[2, 2, 2] = 0 * eta_rhoRe;
Tensor[2, 2, 3] = alphaPlus43 * mu_rhoRe;
//Tensor[2, 2, 4] = 0 * eta_rhoRe;
break;
}
break;
default:
throw new ArgumentOutOfRangeException("dimension");
}
}
/// <summary>
/// Defines the force which is integrated over an immersed boundary,
/// called by <see cref="IBMQueries.LiftOrDragForce"/>
/// </summary>
/// <param name="density"></param>
/// <param name="momentum"></param>
/// <param name="energy"></param>
/// <param name="speciesMap"></param>
/// <param name="direction">Direction of the force projection, e.g. 0=x-axis, 1=y-axis</param>
/// <param name="cutCellMask">Cells intersected by the interface</param>
/// <returns></returns>
static ScalarFunctionEx GetSurfaceForce(
DGField density, VectorField <DGField> momentum, DGField energy, ImmersedSpeciesMap speciesMap, int direction, CellMask cutCellMask)
{
return(delegate(int j0, int Len, NodeSet nodes, MultidimensionalArray result) {
int noOfNodes = nodes.GetLength(0);
int D = nodes.SpatialDimension;
double Reynolds = speciesMap.Control.ReynoldsNumber;
double Mach = speciesMap.Control.MachNumber;
double gamma = speciesMap.Control.EquationOfState.HeatCapacityRatio;
double MachScaling = gamma * Mach * Mach;
MultidimensionalArray rho = MultidimensionalArray.Create(Len, noOfNodes);
density.Evaluate(j0, Len, nodes, rho);
MultidimensionalArray[] m = new MultidimensionalArray[CNSEnvironment.NumberOfDimensions];
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
m[d] = MultidimensionalArray.Create(Len, noOfNodes);
momentum[d].Evaluate(j0, Len, nodes, m[d]);
}
MultidimensionalArray rhoE = MultidimensionalArray.Create(Len, noOfNodes);
energy.Evaluate(j0, Len, nodes, rhoE);
MultidimensionalArray gradRho = MultidimensionalArray.Create(Len, noOfNodes, D);
density.EvaluateGradient(j0, Len, nodes, gradRho);
MultidimensionalArray gradM = MultidimensionalArray.Create(Len, noOfNodes, D, D);
for (int d = 0; d < D; d++)
{
momentum[d].EvaluateGradient(
j0,
Len,
nodes,
gradM.ExtractSubArrayShallow(-1, -1, d, -1),
0,
0.0);
}
MultidimensionalArray normals = speciesMap.Tracker.DataHistories[0].Current.GetLevelSetNormals(nodes, j0, Len);
Vector3D mVec = new Vector3D();
for (int i = 0; i < Len; i++)
{
for (int j = 0; j < noOfNodes; j++)
{
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
mVec[d] = m[d][i, j];
}
Material material = speciesMap.GetMaterial(double.NaN);
StateVector state = new StateVector(material, rho[i, j], mVec, rhoE[i, j]);
double mu = 0.0;
if (Reynolds != 0.0)
{
mu = state.GetViscosity(j0 + j) / Reynolds;
}
double[,] gradU = new double[D, D];
for (int d1 = 0; d1 < D; d1++)
{
for (int d2 = 0; d2 < D; d2++)
{
// Apply chain rule
gradU[d1, d2] = (gradM[i, j, d1, d2] - state.Momentum[d1] / state.Density * gradRho[i, j, d2]) / state.Density;
}
}
double divU = gradU[0, 0] + gradU[1, 1];
switch (direction)
{
// Attention: Changed sign, because normal vector is pointing inwards, not outwards!
case 0: // x-Direction
result[i, j, 0] = -state.Pressure / MachScaling * normals[i, j, 0]
+ mu * (2.0 * gradU[0, 0] - 2.0 / 3.0 * divU) * normals[i, j, 0] //tau_11 * n_1
+ mu * (gradU[0, 1] + gradU[1, 0]) * normals[i, j, 1]; //tau_12 * n_2
break;
case 1: // y-Direction
result[i, j, 0] = -state.Pressure / MachScaling * normals[i, j, 1]
+ mu * (gradU[0, 1] + gradU[1, 0]) * normals[i, j, 0] //tau_12 * n_1
+ mu * (2.0 * gradU[1, 1] - 2.0 / 3.0 * divU) * normals[i, j, 1]; //tau_22*n_2
break;
default:
throw new ArgumentException("Lift and Drag currently only in 2D implemented");
}
}
}
});
}