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);
}
