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implementation of closed 1D and 2D cases
This commit is contained in:
philippun
parent
4108038a62
commit
f1b5138bcc
@ -35,10 +35,14 @@ int main(int argc, char *argv[]) {
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// create a boundary with constant values
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Boundary bc = Boundary(grid);
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bc.setBoundarySideConstant(BC_SIDE_LEFT, 0);
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bc.setBoundarySideConstant(BC_SIDE_RIGHT, 0);
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bc.setBoundarySideConstant(BC_SIDE_TOP, 0);
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bc.setBoundarySideConstant(BC_SIDE_BOTTOM, 0);
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bc.setBoundarySideClosed(BC_SIDE_LEFT);
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bc.setBoundarySideClosed(BC_SIDE_RIGHT);
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bc.setBoundarySideClosed(BC_SIDE_TOP);
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bc.setBoundarySideClosed(BC_SIDE_BOTTOM);
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// bc.setBoundarySideConstant(BC_SIDE_LEFT, 0);
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// bc.setBoundarySideConstant(BC_SIDE_RIGHT, 0);
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// bc.setBoundarySideConstant(BC_SIDE_TOP, 0);
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// bc.setBoundarySideConstant(BC_SIDE_BOTTOM, 0);
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// (optional) set boundary condition values for one side, e.g.:
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235
src/BTCSv2.cpp
235
src/BTCSv2.cpp
@ -4,16 +4,71 @@
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using namespace Eigen;
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static SparseMatrix<double> createCoeffMatrix(MatrixXd &alpha, int numCols, int rowIndex, double sx) {
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static tuple<double, double> calcLeftBoundaryCoeffConstant(MatrixXd &alpha, int &rowIndex, double &sx) {
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double centerCoeff;
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double rightCoeff;
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centerCoeff = 1 + sx * (calcAlphaIntercell(alpha(rowIndex,0), alpha(rowIndex,1))
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+ 2 * alpha(rowIndex,0));
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rightCoeff = -sx * calcAlphaIntercell(alpha(rowIndex,0), alpha(rowIndex,1));
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return {centerCoeff, rightCoeff};
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}
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static tuple<double, double> calcLeftBoundaryCoeffClosed(MatrixXd &alpha, int &rowIndex, double &sx) {
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double centerCoeff;
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double rightCoeff;
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centerCoeff = 1 + sx * calcAlphaIntercell(alpha(rowIndex,0), alpha(rowIndex,1));
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rightCoeff = -sx * calcAlphaIntercell(alpha(rowIndex,0), alpha(rowIndex,1));
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return {centerCoeff, rightCoeff};
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}
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static tuple<double, double> calcRightBoundaryCoeffConstant(MatrixXd &alpha, int &rowIndex, int &n, double &sx) {
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double leftCoeff;
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double centerCoeff;
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leftCoeff = -sx * calcAlphaIntercell(alpha(rowIndex,n-1), alpha(rowIndex,n));
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centerCoeff = 1 + sx * (calcAlphaIntercell(alpha(rowIndex,n-1), alpha(rowIndex,n))
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+ 2 * alpha(rowIndex,n));
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return {leftCoeff, centerCoeff};
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}
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static tuple<double, double> calcRightBoundaryCoeffClosed(MatrixXd &alpha, int &rowIndex, int &n, double &sx) {
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double leftCoeff;
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double centerCoeff;
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leftCoeff = -sx * calcAlphaIntercell(alpha(rowIndex,n-1), alpha(rowIndex,n));
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centerCoeff = 1 + sx * calcAlphaIntercell(alpha(rowIndex,n-1), alpha(rowIndex,n));
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return {leftCoeff, centerCoeff};
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}
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static SparseMatrix<double> createCoeffMatrix(MatrixXd &alpha, vector<BoundaryElement> bcLeft, vector<BoundaryElement> bcRight, int numCols, int rowIndex, double sx) {
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// square matrix of column^2 dimension for the coefficients
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SparseMatrix<double> cm(numCols, numCols);
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cm.reserve(VectorXi::Constant(numCols, 3));
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// left column
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cm.insert(0,0) = 1 + sx * (calcAlphaIntercell(alpha(rowIndex,0), alpha(rowIndex,1))
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+ 2 * alpha(rowIndex,0));
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cm.insert(0,1) = -sx * calcAlphaIntercell(alpha(rowIndex,0), alpha(rowIndex,1));
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BC_TYPE type = bcLeft[rowIndex].getType();
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if (type == BC_TYPE_CONSTANT) {
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auto [centerCoeffTop, rightCoeffTop] = calcLeftBoundaryCoeffConstant(alpha, rowIndex, sx);
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cm.insert(0,0) = centerCoeffTop;
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cm.insert(0,1) = rightCoeffTop;
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} else if (type == BC_TYPE_CLOSED) {
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auto [centerCoeffTop, rightCoeffTop] = calcLeftBoundaryCoeffClosed(alpha, rowIndex, sx);
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cm.insert(0,0) = centerCoeffTop;
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cm.insert(0,1) = rightCoeffTop;
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} else {
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throw_invalid_argument("Undefined Boundary Condition Type somewhere on Left or Top!");
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}
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// inner columns
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int n = numCols-1;
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@ -28,22 +83,101 @@ static SparseMatrix<double> createCoeffMatrix(MatrixXd &alpha, int numCols, int
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}
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// right column
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cm.insert(n,n-1) = -sx * calcAlphaIntercell(alpha(rowIndex,n-1), alpha(rowIndex,n));
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cm.insert(n,n) = 1 + sx * (calcAlphaIntercell(alpha(rowIndex,n-1), alpha(rowIndex,n))
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+ 2 * alpha(rowIndex,n));
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type = bcRight[rowIndex].getType();
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if (type == BC_TYPE_CONSTANT) {
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auto [leftCoeffBottom, centerCoeffBottom] = calcRightBoundaryCoeffConstant(alpha, rowIndex, n, sx);
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cm.insert(n,n-1) = leftCoeffBottom;
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cm.insert(n,n) = centerCoeffBottom;
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} else if (type == BC_TYPE_CLOSED) {
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auto [leftCoeffBottom, centerCoeffBottom] = calcRightBoundaryCoeffClosed(alpha, rowIndex, n, sx);
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cm.insert(n,n-1) = leftCoeffBottom;
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cm.insert(n,n) = centerCoeffBottom;
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} else {
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throw_invalid_argument("Undefined Boundary Condition Type somewhere on Right or Bottom!");
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}
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cm.makeCompressed();
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cm.makeCompressed(); // important for Eigen solver
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return cm;
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}
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static double calcExplicitConcentrationsTopBoundaryConstant(MatrixXd &concentrations,
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MatrixXd &alpha, vector<BoundaryElement> &bcTop, int &rowIndex, int &i, double &sy) {
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double c;
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c = sy * calcAlphaIntercell(alpha(rowIndex,i), alpha(rowIndex+1,i))
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* concentrations(rowIndex,i)
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+ (
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1 - sy * (
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calcAlphaIntercell(alpha(rowIndex,i), alpha(rowIndex+1,i))
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+ 2 * alpha(rowIndex,i)
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)
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) * concentrations(rowIndex,i)
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+ sy * alpha(rowIndex,i) * bcTop[i].getValue();
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return c;
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}
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static double calcExplicitConcentrationsTopBoundaryClosed(MatrixXd &concentrations,
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MatrixXd &alpha, int &rowIndex, int &i, double &sy) {
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double c;
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c = sy * calcAlphaIntercell(alpha(rowIndex,i), alpha(rowIndex+1,i))
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* concentrations(rowIndex,i)
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+ (
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1 - sy * (
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calcAlphaIntercell(alpha(rowIndex,i), alpha(rowIndex+1,i))
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)
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) * concentrations(rowIndex,i);
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return c;
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}
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static double calcExplicitConcentrationsBottomBoundaryConstant(MatrixXd &concentrations,
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MatrixXd &alpha, vector<BoundaryElement> &bcBottom, int &rowIndex, int &i, double &sy) {
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double c;
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c = sy * alpha(rowIndex,i) * bcBottom[i].getValue()
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+ (
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1 - sy * (
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2 * alpha(rowIndex,i)
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+ calcAlphaIntercell(alpha(rowIndex-1,i), alpha(rowIndex,i))
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)
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) * concentrations(rowIndex,i)
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+ sy * calcAlphaIntercell(alpha(rowIndex-1,i), alpha(rowIndex,i))
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* concentrations(rowIndex-1,i);
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return c;
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}
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static double calcExplicitConcentrationsBottomBoundaryClosed(MatrixXd &concentrations,
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MatrixXd &alpha, int &rowIndex, int &i, double &sy) {
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double c;
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c = (
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1 - sy * (
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+ calcAlphaIntercell(alpha(rowIndex-1,i), alpha(rowIndex,i))
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)
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) * concentrations(rowIndex,i)
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+ sy * calcAlphaIntercell(alpha(rowIndex-1,i), alpha(rowIndex,i))
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* concentrations(rowIndex-1,i);
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return c;
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}
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static VectorXd createSolutionVector(MatrixXd &concentrations, MatrixXd &alphaX, MatrixXd &alphaY,
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VectorXd &bcLeft, VectorXd &bcRight, VectorXd &bcTop,
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VectorXd &bcBottom, int length, int rowIndex, double sx, double sy) {
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vector<BoundaryElement> &bcLeft, vector<BoundaryElement> &bcRight,
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vector<BoundaryElement> &bcTop, vector<BoundaryElement> &bcBottom,
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int length, int rowIndex, double sx, double sy) {
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VectorXd sv(length);
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int numRows = concentrations.rows();
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BC_TYPE type;
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// inner rows
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if (rowIndex > 0 && rowIndex < numRows-1) {
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@ -65,40 +199,40 @@ static VectorXd createSolutionVector(MatrixXd &concentrations, MatrixXd &alphaX,
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// first row
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if (rowIndex == 0) {
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for (int i = 0; i < length; i++) {
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sv(i) = sy * calcAlphaIntercell(alphaY(rowIndex,i), alphaY(rowIndex+1,i))
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* concentrations(rowIndex,i)
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+ (
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1 - sy * (
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calcAlphaIntercell(alphaY(rowIndex,i), alphaY(rowIndex+1,i))
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+ 2 * alphaY(rowIndex,i)
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)
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) * concentrations(rowIndex,i)
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+ sy * alphaY(rowIndex,i) * bcTop(i)
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;
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type = bcTop[i].getType();
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if (type == BC_TYPE_CONSTANT) {
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sv(i) = calcExplicitConcentrationsTopBoundaryConstant(concentrations, alphaY, bcTop, rowIndex, i, sy);
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} else if (type == BC_TYPE_CLOSED) {
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sv(i) = calcExplicitConcentrationsTopBoundaryClosed(concentrations, alphaY, rowIndex, i, sy);
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} else {
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throw_invalid_argument("Undefined Boundary Condition Type somewhere on Left or Top!");
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}
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}
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}
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// last row
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if (rowIndex == numRows-1) {
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for (int i = 0; i < length; i++) {
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sv(i) = sy * alphaY(rowIndex,i) * bcBottom(i)
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+ (
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1 - sy * (
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2 * alphaY(rowIndex,i)
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+ calcAlphaIntercell(alphaY(rowIndex-1,i), alphaY(rowIndex,i))
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)
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) * concentrations(rowIndex,i)
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+ sy * calcAlphaIntercell(alphaY(rowIndex-1,i), alphaY(rowIndex,i))
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* concentrations(rowIndex-1,i)
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;
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type = bcBottom[i].getType();
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if (type == BC_TYPE_CONSTANT) {
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sv(i) = calcExplicitConcentrationsBottomBoundaryConstant(concentrations, alphaY, bcBottom, rowIndex, i, sy);
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} else if (type == BC_TYPE_CLOSED) {
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sv(i) = calcExplicitConcentrationsBottomBoundaryClosed(concentrations, alphaY, rowIndex, i, sy);
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} else {
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throw_invalid_argument("Undefined Boundary Condition Type somewhere on Right or Bottom!");
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}
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}
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}
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// first column -> additional fixed concentration change from perpendicular dimension
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sv(0) += 2 * sx * alphaX(rowIndex,0) * bcLeft(rowIndex);
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// first column -> additional fixed concentration change from perpendicular dimension in constant bc case
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if (bcLeft[rowIndex].getType() == BC_TYPE_CONSTANT) {
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sv(0) += 2 * sx * alphaX(rowIndex,0) * bcLeft[rowIndex].getValue();
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}
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// last column -> additional fixed concentration change from perpendicular dimension
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sv(length-1) += 2 * sx * alphaX(rowIndex,length-1) * bcRight(rowIndex);
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// last column -> additional fixed concentration change from perpendicular dimension in constant bc case
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if (bcRight[rowIndex].getType() == BC_TYPE_CONSTANT) {
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sv(length-1) += 2 * sx * alphaX(rowIndex,length-1) * bcRight[rowIndex].getValue();
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}
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return sv;
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}
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@ -124,16 +258,20 @@ static void BTCS_1D(Grid &grid, Boundary &bc, double ×tep) {
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VectorXd b(length);
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MatrixXd alpha = grid.getAlpha();
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VectorXd bcLeft = bc.getBoundarySideValues(BC_SIDE_LEFT);
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VectorXd bcRight = bc.getBoundarySideValues(BC_SIDE_RIGHT);
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vector<BoundaryElement> bcLeft = bc.getBoundarySide(BC_SIDE_LEFT);
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vector<BoundaryElement> bcRight = bc.getBoundarySide(BC_SIDE_RIGHT);
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MatrixXd concentrations = grid.getConcentrations();
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A = createCoeffMatrix(alpha, length, 0, sx); // this is exactly same as in 2D
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A = createCoeffMatrix(alpha, bcLeft, bcRight, length, 0, sx); // this is exactly same as in 2D
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for (int i = 0; i < length; i++) {
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b(i) = concentrations(0,i); // TODO check if this is really the only thing on right hand side of equation in 1D?
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b(i) = concentrations(0,i);
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}
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if (bc.getBoundaryElementType(BC_SIDE_LEFT, 0) == BC_TYPE_CONSTANT) {
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b(0) += 2 * sx * alpha(0,0) * bcLeft[0].getValue();
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}
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if (bc.getBoundaryElementType(BC_SIDE_RIGHT, 0) == BC_TYPE_CONSTANT) {
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b(length-1) += 2 * sx * alpha(0,length-1) * bcRight[0].getValue();
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}
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b(0) += 2 * sx * alpha(0,0) * bcLeft(0);
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b(length-1) += 2 * sx * alpha(0,length-1) * bcRight(0);
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concentrations_t1 = solve(A, b);
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@ -160,21 +298,21 @@ static void BTCS_2D(Grid &grid, Boundary &bc, double ×tep) {
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MatrixXd alphaX = grid.getAlphaX();
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MatrixXd alphaY = grid.getAlphaY();
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VectorXd bcLeft = bc.getBoundarySideValues(BC_SIDE_LEFT);
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VectorXd bcRight = bc.getBoundarySideValues(BC_SIDE_RIGHT);
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VectorXd bcTop = bc.getBoundarySideValues(BC_SIDE_TOP);
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VectorXd bcBottom = bc.getBoundarySideValues(BC_SIDE_BOTTOM);
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vector<BoundaryElement> bcLeft = bc.getBoundarySide(BC_SIDE_LEFT);
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vector<BoundaryElement> bcRight = bc.getBoundarySide(BC_SIDE_RIGHT);
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vector<BoundaryElement> bcTop = bc.getBoundarySide(BC_SIDE_TOP);
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vector<BoundaryElement> bcBottom = bc.getBoundarySide(BC_SIDE_BOTTOM);
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MatrixXd concentrations = grid.getConcentrations();
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for (int i = 0; i < rowMax; i++) {
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A = createCoeffMatrix(alphaX, colMax, i, sx);
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A = createCoeffMatrix(alphaX, bcLeft, bcRight, colMax, i, sx);
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b = createSolutionVector(concentrations, alphaX, alphaY, bcLeft, bcRight,
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bcTop, bcBottom, colMax, i, sx, sy);
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row_t1 = solve(A, b);
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for (int j = 0; j < colMax; j++) {
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concentrations_t1(i,j) = row_t1(j);
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concentrations_t1(i,j) = row_t1(j); // TODO Eigen seq ??
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}
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}
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@ -184,13 +322,14 @@ static void BTCS_2D(Grid &grid, Boundary &bc, double ×tep) {
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alphaY.transposeInPlace();
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for (int i = 0; i < colMax; i++) {
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A = createCoeffMatrix(alphaY, rowMax, i, sy);
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// swap alphas, boundary conditions and sx/sy for column-wise calculation
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A = createCoeffMatrix(alphaY, bcLeft, bcRight, rowMax, i, sy);
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b = createSolutionVector(concentrations_t1, alphaY, alphaX, bcTop, bcBottom,
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bcLeft, bcRight, rowMax, i, sy, sx);
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row_t1 = solve(A, b);
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for (int j = 0; j < rowMax; j++) {
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concentrations(i,j) = row_t1(j);
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concentrations(i,j) = row_t1(j); // TODO Eigen seq ??
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}
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}
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concentrations.transposeInPlace();
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