def _buildMatrix(self, var, SparseMatrix, boundaryCondtions=(), dt=None, equation=None): oldArray = var.getOld() mesh = var.getMesh() NCells = mesh.getNumberOfCells() NCellFaces = mesh._getMaxFacesPerCell() cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0) cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0) cellToCellIDs = mesh._getCellToCellIDs() if NCells > 0: cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs) adjacentValues = numerix.take(oldArray, cellToCellIDs) differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh) differences = MA.filled(differences, 0) minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells)))**2, axis=0)) maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells)))**2, axis=0)) coeff = numerix.array(self._getGeomCoeff(mesh)) coeffXdiffereneces = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq) else: coeffXdiffereneces = 0. return (SparseMatrix(mesh=var.getMesh()), -coeffXdiffereneces * mesh.getCellVolumes())
def _calcValue_(self, alpha, id1, id2): cell1 = numerix.take(self.var, id1, axis=-1) cell2 = numerix.take(self.var, id2, axis=-1) return numerix.where((cell1 > 0) & (cell2 > 0), numerix.minimum(cell1, cell2), numerix.where((cell1 < 0) & (cell2 < 0), numerix.maximum(cell1, cell2), 0))
def _getOldAdjacentValues(self, oldArray, id1, id2, dt): oldArray1, oldArray2 = ExplicitUpwindConvectionTerm._getOldAdjacentValues(self, oldArray, id1, id2, dt) mesh = oldArray.getMesh() interiorIDs = numerix.nonzero(mesh.getInteriorFaces())[0] interiorFaceAreas = numerix.take(mesh._getFaceAreas(), interiorIDs) interiorFaceNormals = numerix.take(mesh._getOrientedFaceNormals(), interiorIDs, axis=-1) # Courant-Friedrichs-Levy number interiorCFL = abs(numerix.take(self._getGeomCoeff(mesh), interiorIDs)) * dt gradUpwind = (oldArray2 - oldArray1) / numerix.take(mesh._getCellDistances(), interiorIDs) vol1 = numerix.take(mesh.getCellVolumes(), id1) self.CFL = interiorCFL / vol1 oldArray1 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.getGrad(), id1, axis=-1), interiorFaceNormals), gradUpwind) \ * (vol1 - interiorCFL) / interiorFaceAreas vol2 = numerix.take(mesh.getCellVolumes(), id2) self.CFL = numerix.maximum(interiorCFL / vol2, self.CFL) oldArray2 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.getGrad(), id2, axis=-1), -interiorFaceNormals), -gradUpwind) \ * (vol2 - interiorCFL) / interiorFaceAreas return oldArray1, oldArray2
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, equation=None, transientGeomCoeff=None, diffusionGeomCoeff=None): oldArray = var.old mesh = var.mesh NCells = mesh.numberOfCells NCellFaces = mesh._maxFacesPerCell cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0) cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0) cellToCellIDs = mesh._cellToCellIDs if NCells > 0: cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs) adjacentValues = numerix.take(oldArray, cellToCellIDs) differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh) differences = MA.filled(differences, 0) minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0)) maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0)) coeff = numerix.array(self._getGeomCoeff(var)) coeffXdiffereneces = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq) else: coeffXdiffereneces = 0. return (var, SparseMatrix(mesh=var.mesh), -coeffXdiffereneces * mesh.cellVolumes)
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, equation=None, transientGeomCoeff=None, diffusionGeomCoeff=None): oldArray = var.old mesh = var.mesh NCells = mesh.numberOfCells NCellFaces = mesh._maxFacesPerCell cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0) cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0) cellToCellIDs = mesh._cellToCellIDs if NCells > 0: cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs) adjacentValues = numerix.take(oldArray, cellToCellIDs) differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh) differences = MA.filled(differences, 0) minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0)) maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0)) coeff = numerix.array(self._getGeomCoeff(var)) coeffXdifferences = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq) else: coeffXdifferences = 0. return (var, SparseMatrix(mesh=var.mesh), -coeffXdifferences * mesh.cellVolumes)
def _calcValue_(self, alpha, id1, id2): cell1 = numerix.take(self.var,id1, axis=-1) cell2 = numerix.take(self.var,id2, axis=-1) return numerix.where((cell1 > 0) & (cell2 > 0), numerix.minimum(cell1, cell2), numerix.where((cell1 < 0) & (cell2 < 0), numerix.maximum(cell1, cell2), 0))
def _getNonOrthogonality(self): exteriorFaceArray = numerix.zeros((self.faceCellIDs.shape[1],)) numerix.put(exteriorFaceArray, numerix.nonzero(self.getExteriorFaces()), 1) unmaskedFaceCellIDs = MA.filled(self.faceCellIDs, 0) ## what we put in for the "fill" doesn't matter because only exterior faces have anything masked, and exterior faces have their displacement vectors set to zero. ## if it's an exterior face, make the "displacement vector" equal to zero so the cross product will be zero. faceDisplacementVectors = numerix.where(numerix.array(zip(exteriorFaceArray, exteriorFaceArray)), 0.0, numerix.take(self._getCellCenters().swapaxes(0,1), unmaskedFaceCellIDs[1, :]) - numerix.take(self._getCellCenters().swapaxes(0,1), unmaskedFaceCellIDs[0, :])).swapaxes(0,1) faceCrossProducts = (faceDisplacementVectors[0, :] * self.faceNormals[1, :]) - (faceDisplacementVectors[1, :] * self.faceNormals[0, :]) faceDisplacementVectorLengths = numerix.maximum(((faceDisplacementVectors[0, :] ** 2) + (faceDisplacementVectors[1, :] ** 2)) ** 0.5, 1.e-100) faceWeightedNonOrthogonalities = abs(faceCrossProducts / faceDisplacementVectorLengths) * self.faceAreas cellFaceWeightedNonOrthogonalities = numerix.take(faceWeightedNonOrthogonalities, self.cellFaceIDs) cellFaceAreas = numerix.take(self.faceAreas, self.cellFaceIDs) cellTotalWeightedValues = numerix.add.reduce(cellFaceWeightedNonOrthogonalities, axis = 0) cellTotalFaceAreas = numerix.add.reduce(cellFaceAreas, axis = 0) return (cellTotalWeightedValues / cellTotalFaceAreas)
def _nonOrthogonality(self): exteriorFaceArray = numerix.zeros((self.faceCellIDs.shape[1], ), 'l') numerix.put(exteriorFaceArray, numerix.nonzero(self.exteriorFaces), 1) unmaskedFaceCellIDs = MA.filled(self.faceCellIDs, 0) # what we put in for the "fill" doesn't matter because only exterior # faces have anything masked, and exterior faces have their displacement # vectors set to zero. # # if it's an exterior face, make the "displacement vector" equal to zero # so the cross product will be zero. faceDisplacementVectors = \ numerix.where(numerix.array(zip(exteriorFaceArray, exteriorFaceArray)), 0.0, numerix.take(self._scaledCellCenters.swapaxes(0,1), unmaskedFaceCellIDs[1, :]) \ - numerix.take(self._scaledCellCenters.swapaxes(0,1), unmaskedFaceCellIDs[0, :])) faceDisplacementVectors = faceDisplacementVectors.swapaxes(0, 1) faceCrossProducts = (faceDisplacementVectors[0, :] * self.faceNormals[1,:]) \ - (faceDisplacementVectors[1, :] * self.faceNormals[0, :]) faceDisplacementVectorLengths = numerix.maximum(((faceDisplacementVectors[0, :] ** 2) \ + (faceDisplacementVectors[1, :] ** 2)) ** 0.5, 1.e-100) faceWeightedNonOrthogonalities = abs( faceCrossProducts / faceDisplacementVectorLengths) * self._faceAreas cellFaceWeightedNonOrthogonalities = numerix.take( faceWeightedNonOrthogonalities, self.cellFaceIDs) cellFaceAreas = numerix.take(self._faceAreas, self.cellFaceIDs) cellTotalWeightedValues = numerix.add.reduce( cellFaceWeightedNonOrthogonalities, axis=0) cellTotalFaceAreas = numerix.add.reduce(cellFaceAreas, axis=0) return (cellTotalWeightedValues / cellTotalFaceAreas)