/// <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); }); }