private static double GetDY(DoubleMatrix3D data, int i, int j, int k, NumericalParameters numPar) { if (j == 0) return (GetValue(data, i, j + 1, k) - GetValue(data, i, j, k)) / numPar.Dy; else if (j == numPar.Ny - 1) return (GetValue(data, i, j, k) - GetValue(data, i, j - 1, k)) / numPar.Dy; else return (GetValue(data, i, j + 1, k) - GetValue(data, i, j - 1, k)) / (2 * numPar.Dy); }
private static double GetDZ(DoubleMatrix3D data, int i, int j, int k, NumericalParameters numPar) { if (k == 0) return (GetValue(data, i, j, k + 1) - GetValue(data, i, j, k)) / numPar.Dz; else if (k == numPar.Nz - 1) return (GetValue(data, i, j, k) - GetValue(data, i, j, k - 1)) / numPar.Dz; else return (GetValue(data, i, j, k + 1) - GetValue(data, i, j, k - 1)) / (2 * numPar.Dz); }
private static double GetDX(DoubleMatrix3D data, int i, int j, int k, NumericalParameters numPar) { if (i == 0) return (GetValue(data, i + 1, j, k) - GetValue(data, i, j, k)) / numPar.Dx; else if (i == numPar.Nx - 1) return (GetValue(data, i, j, k) - GetValue(data, i - 1, j, k)) / numPar.Dx; else return (GetValue(data, i + 1, j, k) - GetValue(data, i - 1, j, k)) / (2 * numPar.Dx); }
public static double GetPhiZ(DoubleMatrix3D u, DoubleMatrix3D v, DoubleMatrix3D w, int i, int j, int k, NumericalParameters numPar) { double u_z = GetDZ(u, i, j, k, numPar); double v_z = GetDZ(v, i, j, k, numPar); double w_z = GetDZ(w, i, j, k, numPar); double w_x = GetDX(w, i, j, k, numPar); double w_y = GetDY(w, i, j, k, numPar); return u_z * u_z + v_z * v_z + 2 * w_z * w_z + u_z * w_x + w_y * v_z; }
public static double GetPhiY(DoubleMatrix3D u, DoubleMatrix3D v, DoubleMatrix3D w, int i, int j, int k, NumericalParameters numPar) { double u_y = GetDY(u, i, j, k, numPar); double v_y = GetDY(v, i, j, k, numPar); double w_y = GetDY(w, i, j, k, numPar); double v_x = GetDX(v, i, j, k, numPar); double v_z = GetDZ(v, i, j, k, numPar); return u_y * u_y + 2 * v_y * v_y + w_y * w_y + u_y * v_x + w_y * v_z; }
public static double GetPhiX(DoubleMatrix3D u, DoubleMatrix3D v, DoubleMatrix3D w, int i, int j, int k, NumericalParameters numPar) { double u_x = GetDX(u, i, j, k, numPar); double v_x = GetDX(v, i, j, k, numPar); double w_x = GetDX(w, i, j, k, numPar); double u_y = GetDY(u, i, j, k, numPar); double u_z = GetDZ(u, i, j, k, numPar); return 2 * u_x * u_x + v_x * v_x + w_x * w_x + v_x * u_y + w_x * u_z; }
public static double GetValue(DoubleMatrix3D data, int i, int j, int k) { return (data.FirstMatrix[i, j, k] + data.SecondMatrix[i, j, k]) / 2.0; }
private void SolveColumnX(int i, int j, int startIndex, int endIndex, LayerData oldLayer, LayerData prevLayer, LayerData nextLayer, bool state) { DoubleMatrix3D u = new DoubleMatrix3D { FirstMatrix = oldLayer.U, SecondMatrix = prevLayer.U }; DoubleMatrix3D v = new DoubleMatrix3D { FirstMatrix = oldLayer.V, SecondMatrix = prevLayer.V }; DoubleMatrix3D w = new DoubleMatrix3D { FirstMatrix = oldLayer.W, SecondMatrix = prevLayer.W }; DoubleMatrix3D T = new DoubleMatrix3D { FirstMatrix = oldLayer.T, SecondMatrix = prevLayer.T }; int length = endIndex - startIndex; double[] downRow = new double[length]; double[] middleRow = new double[length]; double[] upperRow = new double[length]; double[] f = new double[length]; //Solving for U double h = 1.0 / (numPar.Re * numPar.Dx * numPar.Dx); for (int k = 1; k < length - 1; k++) { if (i == 0 || i == height - 1 || j == Az || j == Dz - 1) { downRow[k] = 0.0; middleRow[k] = 1.0; upperRow[k] = 0.0; f[k] = 0.0; } else { downRow[k] = Auxiliaries.GetValue(u, startIndex + k, i, j) / (2 * numPar.Dx) - h; middleRow[k] = 3.0 / numPar.Dt + 2.0 * h; upperRow[k] = -Auxiliaries.GetValue(u, startIndex + k, i, j) / (2.0 * numPar.Dx) - h; f[k] = 3.0 * prevLayer.U[startIndex + k, i, j] / numPar.Dt - (Auxiliaries.GetValue(T, startIndex + k + 1, i, j) - Auxiliaries.GetValue(T, startIndex + k - 1, i, j)) / (2.0 * numPar.Dx); } if (column) if ((j == Bz || j == Cz - 1) && (k >= Bx && k <= Cx - 1)) { downRow[k] = 0.0; middleRow[k] = 1.0; upperRow[k] = 0.0; f[k] = 0.0; } } if (startIndex == Ax && i != 0 && i != height - 1 && j != Az && j != Dz - 1) f[0] = 1.0; else f[0] = 0.0; upperRow[0] = 0.0; middleRow[0] = 1.0; downRow[0] = 0.0; if (!state) { f[length - 1] = 0.0; upperRow[length - 1] = 0.0; middleRow[length - 1] = 1.0; downRow[length - 1] = 0.0; } else { f[length - 1] = 2.0 * prevLayer.U[length - 2, i, j] - prevLayer.U[length - 3, i, j]; upperRow[length - 1] = 0.0; middleRow[length - 1] = 1.0; downRow[length - 1] = 0.0; } PurlinMatrix pmatrix = new PurlinMatrix(downRow, middleRow, upperRow); PurlinSolver pSolver = new PurlinSolver(pmatrix, f); double[] result = pSolver.Solve(); nextLayer.U.SetColumn(i, j, startIndex, Dimensions.Width, result); //if (state) // nextLayer.U[length - 1, i, j] = 2.0 * nextLayer.U[length - 2, i, j] - nextLayer.U[length - 3, i, j]; //Solving for V for (int k = 1; k < length - 1; k++) { if (i == 0 || i == height - 1 || j == Az || j == Dz - 1) f[k] = 0.0; else f[k] = 3 * prevLayer.V[startIndex + k, i, j] / numPar.Dt; if (column) if ((j == Bz || j == Cz - 1) && (k >= Bx && k <= Cx - 1)) f[k] = 0.0; } f[0] = 0.0; if (!state) f[length - 1] = 0.0; else f[length - 1] = 2.0 * prevLayer.V[length - 2, i, j] - prevLayer.V[length - 3, i, j]; pSolver = new PurlinSolver(pmatrix, f); result = pSolver.Solve(); nextLayer.V.SetColumn(i, j, startIndex, Dimensions.Width, result); //if (state) // nextLayer.V[length - 1, i, j] = 2.0 * nextLayer.V[length - 2, i, j] - nextLayer.V[length - 3, i, j]; //Solving for W for (int k = 1; k < length - 1; k++) { if (i == 0 || i == height - 1 || j == Az || j == Dz - 1) f[k] = 0.0; else f[k] = 3 * prevLayer.W[startIndex + k, i, j] / numPar.Dt; if (column) if ((j == Bz || j == Cz - 1) && (k >= Bx && k <= Cx - 1)) f[k] = 0.0; } f[0] = 0.0; if (state) f[length - 1] = 0.0; else f[length - 1] = 2.0 * prevLayer.W[length - 2, i, j] - prevLayer.W[length - 3, i, j]; pSolver = new PurlinSolver(pmatrix, f); result = pSolver.Solve(); nextLayer.W.SetColumn(i, j, startIndex, Dimensions.Width, result); //if (state) // nextLayer.W[length - 1, i, j] = 2.0 * nextLayer.W[length - 2, i, j] - nextLayer.W[length - 3, i, j]; //Solving for T h = 1.0 / (numPar.Re * numPar.Pr * numPar.Dx * numPar.Dx); for (int k = 1; k < length - 1; k++) { upperRow[k] = 0.0; middleRow[k] = 1.0; downRow[k] = 0.0; if (i == 0) f[k] = prevLayer.T[k, i + 1, j]; else if (i == height - 1) f[k] = prevLayer.T[k, i - 1, j]; else if (j == Az) f[k] = oldLayer.T[k, i, j + 1]; else if (j == Dz - 1) f[k] = oldLayer.T[k, i, j - 1]; else { downRow[k] = Auxiliaries.GetValue(u, startIndex + k, i, j) / (2 * numPar.Dx) - h; middleRow[k] = 3.0 / numPar.Dt + 2.0 * h; upperRow[k] = -Auxiliaries.GetValue(u, startIndex + k, i, j) / (2.0 * numPar.Dx) - h; f[k] = 3 * prevLayer.T[startIndex + k, i, j] / numPar.Dt + cp * Auxiliaries.GetPhiX(u, v, w, startIndex + k, i, j, numPar); } if (column) { if ((j == Bz) && (k >= Bx && k <= Cx - 1)) f[k] = oldLayer.T[k, i, j - 1]; else if ((j == Cz - 1) && (k >= Bx && k <= Cx - 1)) f[k] = oldLayer.T[k, i, j + 1]; } } if (startIndex == Ax && i != 0 && i != height - 1 && j != Az && j != Dz - 1) { f[0] = 1.0; upperRow[0] = 0.0; middleRow[0] = 1.0; downRow[0] = 0.0; } else { f[0] = 0.0; upperRow[0] = 1.0; middleRow[0] = -1.0; downRow[0] = 0.0; } if (!state) { upperRow[length - 1] = 0.0; middleRow[length - 1] = -1.0; downRow[length - 1] = 1.0; f[length - 1] = 0.0; } else { upperRow[length - 1] = 0.0; middleRow[length - 1] = 1.0; downRow[length - 1] = 0.0; f[length - 1] = 2.0 * prevLayer.T[length - 2, i, j] - prevLayer.T[length - 3, i, j]; } pmatrix = new PurlinMatrix(downRow, middleRow, upperRow); pSolver = new PurlinSolver(pmatrix, f); result = pSolver.Solve(); nextLayer.T.SetColumn(i, j, startIndex, Dimensions.Width, result); //if (state) // nextLayer.T[length - 1, i, j] = 2.0 * nextLayer.T[length - 2, i, j] - nextLayer.T[length - 3, i, j]; }
private void SolveColumnZ(int i, int j, int startIndex, int endIndex, LayerData oldLayer, LayerData prevLayer, LayerData nextLayer) { DoubleMatrix3D u = new DoubleMatrix3D { FirstMatrix = oldLayer.U, SecondMatrix = prevLayer.U }; DoubleMatrix3D v = new DoubleMatrix3D { FirstMatrix = oldLayer.V, SecondMatrix = prevLayer.V }; DoubleMatrix3D w = new DoubleMatrix3D { FirstMatrix = oldLayer.W, SecondMatrix = prevLayer.W }; DoubleMatrix3D T = new DoubleMatrix3D { FirstMatrix = oldLayer.T, SecondMatrix = prevLayer.T }; int length = endIndex - startIndex; double[] downRow = new double[length]; double[] middleRow = new double[length]; double[] upperRow = new double[length]; double[] f = new double[length]; //Solving for U double h = 1.0 / (numPar.Dz * numPar.Dz * numPar.Re); for (int k = 1; k < length - 1; k++) { downRow[k] = Auxiliaries.GetValue(w, i, j, startIndex + k) / (2.0 * numPar.Dz) - h; middleRow[k] = 3.0 / numPar.Dt + 2.0 * h; upperRow[k] = -Auxiliaries.GetValue(w, i, j, startIndex + k) / (2.0 * numPar.Dz) - h; f[k] = 3.0 * prevLayer.U[i, j, startIndex + k] / numPar.Dt; } upperRow[0] = 0.0; middleRow[0] = 1.0; downRow[0] = 0.0; f[0] = 0.0; upperRow[length - 1] = 0.0; middleRow[length - 1] = 1.0; downRow[length - 1] = 0.0; f[length - 1] = 0.0; PurlinMatrix pmatrix = new PurlinMatrix(downRow, middleRow, upperRow); PurlinSolver pSolver = new PurlinSolver(pmatrix, f); double[] result = pSolver.Solve(); nextLayer.U.SetColumn(i, j, startIndex, Dimensions.Thickness, result); //Solving for V for (int k = 1; k < length - 1; k++) { f[k] = 3.0 * prevLayer.V[i, j, startIndex + k] / numPar.Dt; } f[0] = 0.0; f[length - 1] = 0.0; pSolver = new PurlinSolver(pmatrix, f); result = pSolver.Solve(); nextLayer.V.SetColumn(i, j, startIndex, Dimensions.Thickness, result); //Solving for W for (int k = 1; k < length - 1; k++) { f[k] = 3.0 * prevLayer.W[i, j, startIndex + k] / numPar.Dt - (Auxiliaries.GetValue(T, i, j, startIndex + k + 1) - Auxiliaries.GetValue(T, i, j, startIndex + k - 1)) / (2.0 * numPar.Dz); } f[0] = 0.0; f[length - 1] = 0.0; pSolver = new PurlinSolver(pmatrix, f); result = pSolver.Solve(); nextLayer.W.SetColumn(i, j, startIndex, Dimensions.Thickness, result); //Solving for T h = 1.0 / (numPar.Dz * numPar.Dz * numPar.Re * numPar.Pr); for (int k = 1; k < length - 1; k++) { downRow[k] = Auxiliaries.GetValue(w, i, j, startIndex + k) / (2.0 * numPar.Dz) - h; middleRow[k] = 3.0 / numPar.Dt + 2.0 * h; upperRow[k] = -Auxiliaries.GetValue(w, i, j, startIndex + k) / (2.0 * numPar.Dz) - h; f[k] = 3.0 * prevLayer.T[i, j, startIndex + k] / numPar.Dt + cp * Auxiliaries.GetPhiZ(u, v, w, i, j, startIndex + k, numPar); } upperRow[0] = 1.0; middleRow[0] = -1.0; downRow[0] = 0.0; f[0] = 0.0; upperRow[length - 1] = 0.0; middleRow[length - 1] = -1.0; downRow[length - 1] = 1.0; f[length - 1] = 0; pSolver = new PurlinSolver(pmatrix, f); result = pSolver.Solve(); nextLayer.T.SetColumn(i, j, startIndex, Dimensions.Thickness, result); }