/// <summary>
/// L2 error of some quantity derived from the state vector (e.g.,
/// entropy) with respect to given reference solution. The quadrature
/// is determined from the settings in <see cref="IBMControl"/>
/// </summary>
/// <param name="quantityOfInterest"></param>
/// <param name="referenceSolution"></param>
/// <returns></returns>
public static Query L2Error(Func <StateVector, double> quantityOfInterest, Func <double[], double, double> referenceSolution)
{
return(delegate(IApplication <AppControl> app, double time) {
IProgram <CNSControl> program = app as IProgram <CNSControl>;
if (program == null)
{
throw new Exception();
}
ImmersedSpeciesMap speciesMap = program.SpeciesMap as ImmersedSpeciesMap;
IBMControl control = program.Control as IBMControl;
if (speciesMap == null || control == null)
{
throw new Exception(
"Query is only valid for immersed boundary runs");
}
SpeciesId species = speciesMap.Tracker.GetSpeciesId(control.FluidSpeciesName);
int order = control.LevelSetQuadratureOrder;
CellQuadratureScheme scheme = speciesMap.QuadSchemeHelper.GetVolumeQuadScheme(
species, true, speciesMap.SubGrid.VolumeMask);
var composititeRule = scheme.Compile(program.GridData, order);
IChunkRulePair <QuadRule>[] chunkRulePairs = composititeRule.ToArray();
DGField density = program.WorkingSet.Density;
VectorField <DGField> momentum = program.WorkingSet.Momentum;
DGField energy = program.WorkingSet.Energy;
// Construct dummy field since L2Error is currently only supported
// for Field's; However, _avoid_ a projection.
DGField dummy = new SinglePhaseField(new Basis(program.GridData, 0));
Material material = speciesMap.GetMaterial(double.NaN);
int index = 0;
double value = dummy.LxError(
(ScalarFunctionEx) delegate(int j0, int Len, NodeSet nodes, MultidimensionalArray result) {
MultidimensionalArray input = program.GridData.GlobalNodes.GetValue_Cell(nodes, j0, Len);
Chunk chunk = chunkRulePairs[index].Chunk;
QuadRule rule = chunkRulePairs[index].Rule;
if (chunk.i0 != j0 || chunk.Len != Len)
{
throw new Exception();
}
if (rule.NoOfNodes != nodes.GetLength(0))
{
throw new Exception();
}
MultidimensionalArray rho = MultidimensionalArray.Create(chunk.Len, rule.NoOfNodes);
density.Evaluate(chunk.i0, chunk.Len, nodes, rho);
MultidimensionalArray[] m = new MultidimensionalArray[CNSEnvironment.NumberOfDimensions];
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
m[d] = MultidimensionalArray.Create(chunk.Len, rule.NoOfNodes);
momentum[d].Evaluate(chunk.i0, chunk.Len, nodes, m[d]);
}
MultidimensionalArray rhoE = MultidimensionalArray.Create(chunk.Len, rule.NoOfNodes);
energy.Evaluate(chunk.i0, chunk.Len, nodes, rhoE);
double[] X = new double[CNSEnvironment.NumberOfDimensions];
Vector3D mVec = new Vector3D();
for (int i = 0; i < chunk.Len; i++)
{
for (int j = 0; j < rule.NoOfNodes; j++)
{
for (int d = 0; d < CNSEnvironment.NumberOfDimensions; d++)
{
X[d] = input[i, j, d];
mVec[d] = m[d][i, j];
}
StateVector state = new StateVector(material, rho[i, j], mVec, rhoE[i, j]);
double qoi = quantityOfInterest(state);
Debug.Assert(
!double.IsNaN(qoi),
"Encountered node with unphysical state"
+ " (not able to determine quantity of interest)");
result[i, j] = qoi - referenceSolution(X, time);
}
}
index++;
},
(X, a, b) => (a - b) * (a - b),
composititeRule);
// No value is NaN, but the results. How can this be?
// => All values around 0, but values in void region are a little
// farther away from the exact solution
// => weights in the void zone sum up to something slightly negative
Debug.Assert(
value >= 0,
"Encountered unphysical norm even though individual values where valid."
+ " This indicates a problem with cut-cell quadrature.");
return Math.Sqrt(value);
});
}
