/// <summary>
/// Consistency and penalty term
/// </summary>
void INonlinEdgeForm_V.BoundaryEdge(ref EdgeFormParams efp,
MultidimensionalArray[] Uin, MultidimensionalArray[] GradUin,
MultidimensionalArray fin)
{
int NumOfCells = efp.Len;
Debug.Assert(fin.GetLength(0) == NumOfCells);
int NumOfNodes = fin.GetLength(1); // no of nodes per cell
int dimension = efp.GridDat.SpatialDimension;
for (int cell = 0; cell < NumOfCells; cell++) // loop over cells...
{
int iEdge = efp.e0 + cell;
// Penalty is calculated according to the formula in background cells
int jCellIn = this.GridData.Edges.CellIndices[iEdge, 0];
double penalty = 2 * this.penalties[jCellIn];
byte edgeTag = this.GridData.iGeomEdges.EdgeTags[iEdge];
XDGHeatBcType edgeType = this.boundaryCondMap.EdgeTag2Type[edgeTag];
Func <double[], double, double> dirichletFunction = this.boundaryCondMap.bndFunction["u"][edgeTag];
for (int node = 0; node < NumOfNodes; node++) // loop over nodes...
// Global node coordinates
{
double[] X = new double[dimension];
for (int i = 0; i < dimension; i++)
{
X[i] = efp.NodesGlobal[cell, node, i];
}
// SIPG Flux Loops
double viscosityIn = efp.ParameterVars_IN[0][cell, node];
switch (edgeType)
{
case XDGHeatBcType.Dirichlet:
double g_D = dirichletFunction(X, efp.time);
double flux = 0.0;
for (int d = 0; d < GridData.SpatialDimension; d++)
{
double n = efp.Normals[cell, node, d];
flux -= viscosityIn * GradUin[0][cell, node, d] * n; // Consistency term
}
flux += viscosityIn * (Uin[0][cell, node] - g_D) * penalty; // Penalty term
fin[cell, node] += flux;
break;
default:
// Boundary value is zero neumann boundary, i.e. do nothing
break;
}
}
}
}
/// <summary>
/// Symmetry term
/// </summary>
void INonlinEdgeForm_GradV.BoundaryEdge(ref EdgeFormParams efp,
MultidimensionalArray[] Uin, MultidimensionalArray[] GradUin,
MultidimensionalArray fin)
{
int NumOfCells = efp.Len;
Debug.Assert(fin.GetLength(0) == NumOfCells);
int NumOfNodes = fin.GetLength(1); // no of nodes per cell
int dimension = efp.GridDat.SpatialDimension;
for (int cell = 0; cell < NumOfCells; cell++) // loop over cells...
{
int iEdge = efp.e0 + cell;
byte edgeTag = this.GridData.iGeomEdges.EdgeTags[iEdge];
XDGHeatBcType edgeType = this.boundaryCondMap.EdgeTag2Type[edgeTag];
Func <double[], double, double> dirichletFunction = this.boundaryCondMap.bndFunction["u"][edgeTag];
for (int node = 0; node < NumOfNodes; node++) // loop over nodes...
// Global node coordinates
{
double[] X = new double[dimension];
for (int i = 0; i < dimension; i++)
{
X[i] = efp.NodesGlobal[cell, node, i];
}
switch (edgeType)
{
case XDGHeatBcType.Dirichlet:
double g_D = dirichletFunction(X, efp.time);
//double uJump = 0.5 * (Uin[0][cell, node] - g_D);
double uJump = 1.0 * (Uin[0][cell, node] - g_D);
double fluxIn = efp.ParameterVars_IN[0][cell, node] * uJump;
for (int d = 0; d < GridData.SpatialDimension; d++)
{
double n = efp.Normals[cell, node, d];
fin[cell, node, d] -= fluxIn * n;
}
break;
default:
// Boundary value is zero neumann boundary, i.e. do nothing
break;
}
}
}
}
public override double BoundaryEdgeForm(ref CommonParamsBnd inp, double[] _uA, double[,] _Grad_uA, double _vA, double[] _Grad_vA)
{
double Acc = 0.0;
double pnlty = 2 * this.GetPenalty(inp.jCellIn, -1);
double nuA = this.Nu(inp.X, inp.Parameters_IN, inp.jCellIn);
XDGHeatBcType edgeType = this.boundaryCondMap.EdgeTag2Type[inp.EdgeTag];
switch (edgeType)
{
case XDGHeatBcType.Dirichlet:
Func <double[], double, double> dirichletFunction = this.boundaryCondMap.bndFunction["u"][inp.EdgeTag];
double g_D = dirichletFunction(inp.X, inp.time);
for (int d = 0; d < inp.D; d++)
{
double nd = inp.Normal[d];
Acc += (nuA * _Grad_uA[0, d]) * (_vA) * nd; // consistency
Acc += (nuA * _Grad_vA[d]) * (_uA[0] - g_D) * nd; // symmetry
}
Acc *= this.m_alpha;
Acc -= nuA * (_uA[0] - g_D) * (_vA - 0) * pnlty; // penalty
break;
case XDGHeatBcType.ZeroNeumann:
double g_N = 0.0;
Acc += nuA * g_N * _vA * this.m_alpha; // consistency
break;
default:
throw new NotSupportedException();
}
return(Acc);
}