void GridPatchCartesianGLL::EvaluateGeometricTerms() {
// Physical constants
const PhysicalConstants & phys = m_grid.GetModel().GetPhysicalConstants();
// Obtain Gauss Lobatto quadrature nodes and weights
DataVector<double> dGL;
DataVector<double> dWL;
GaussLobattoQuadrature::GetPoints(m_nHorizontalOrder, 0.0, 1.0, dGL, dWL);
// Obtain normalized areas in the vertical
const DataVector<double> & dWNode =
m_grid.GetREtaLevelsNormArea();
const DataVector<double> & dWREdge =
m_grid.GetREtaInterfacesNormArea();
// Verify that normalized areas are correct
double dWNodeSum = 0.0;
for (int k = 0; k < dWNode.GetRows(); k++) {
dWNodeSum += dWNode[k];
}
if (fabs(dWNodeSum - 1.0) > 1.0e-13) {
_EXCEPTION1("Error in normalized areas (%1.15e)", dWNodeSum);
}
if (m_grid.GetVerticalStaggering() !=
Grid::VerticalStaggering_Interfaces
) {
double dWREdgeSum = 0.0;
for (int k = 0; k < dWREdge.GetRows(); k++) {
dWREdgeSum += dWREdge[k];
}
if (fabs(dWREdgeSum - 1.0) > 1.0e-13) {
_EXCEPTION1("Error in normalized areas (%1.15e)", dWREdgeSum);
}
}
// Derivatives of basis functions
GridCartesianGLL & gridCartesianGLL =
dynamic_cast<GridCartesianGLL &>(m_grid);
const DataMatrix<double> & dDxBasis1D = gridCartesianGLL.GetDxBasis1D();
double dy0 = 0.5 * fabs(m_dGDim[3] - m_dGDim[2]);
double dfp = 2.0 * phys.GetOmega() * sin(m_dRefLat);
double dbetap = 2.0 * phys.GetOmega() * cos(m_dRefLat) /
phys.GetEarthRadius();
// Initialize the Coriolis force at each node
for (int i = 0; i < m_box.GetATotalWidth(); i++) {
for (int j = 0; j < m_box.GetBTotalWidth(); j++) {
// Coriolis force by beta approximation
//m_dataCoriolisF[i][j] = dfp + dbetap * (m_dataLat[i][j] - dy0);
//m_dataCoriolisF[i][j] = dfp;
//m_dataCoriolisF[i][j] = 0.0;
}
}
// Initialize metric and Christoffel symbols in terrain-following coords
for (int a = 0; a < GetElementCountA(); a++) {
for (int b = 0; b < GetElementCountB(); b++) {
for (int i = 0; i < m_nHorizontalOrder; i++) {
for (int j = 0; j < m_nHorizontalOrder; j++) {
// Nodal points
int iElementA = m_box.GetAInteriorBegin() + a * m_nHorizontalOrder;
int iElementB = m_box.GetBInteriorBegin() + b * m_nHorizontalOrder;
int iA = iElementA + i;
int iB = iElementB + j;
// Topography height and its derivatives
double dZs = m_dataTopography[iA][iB];
double dDaZs = m_dataTopographyDeriv[0][iA][iB];
double dDbZs = m_dataTopographyDeriv[1][iA][iB];
// Initialize 2D Jacobian
m_dataJacobian2D[iA][iB] = 1.0;
// Initialize 2D contravariant metric
m_dataContraMetric2DA[iA][iB][0] = 1.0;
m_dataContraMetric2DA[iA][iB][1] = 0.0;
m_dataContraMetric2DB[iA][iB][0] = 0.0;
m_dataContraMetric2DB[iA][iB][1] = 1.0;
// Initialize 2D covariant metric
m_dataCovMetric2DA[iA][iB][0] = 1.0;
m_dataCovMetric2DA[iA][iB][1] = 0.0;
m_dataCovMetric2DB[iA][iB][0] = 0.0;
m_dataCovMetric2DB[iA][iB][1] = 1.0;
// Vertical coordinate transform and its derivatives
for (int k = 0; k < m_grid.GetRElements(); k++) {
// Gal-Chen and Somerville (1975) terrain following coord
// Schar Exponential Decay terrain following coord
double dREta = m_grid.GetREtaLevel(k);
double dREtaStretch;
double dDxREtaStretch;
m_grid.EvaluateVerticalStretchF(
dREta, dREtaStretch, dDxREtaStretch);
//double dZ = dZs + (m_grid.GetZtop() - dZs) * dREtaStretch;
//double dbZ = sinh(m_grid.GetZtop() * (1.0 - dREtaStretch) / m_dSL)
// / sinh(m_grid.GetZtop() / m_dSL);
//double dZ = m_grid.GetZtop() * dREtaStretch + dZs; // * dbZ;
double dZ = dZs + (m_grid.GetZtop() - dZs) * dREtaStretch;
double dDaZ = (1.0 - dREtaStretch) * dDaZs;
double dDbZ = (1.0 - dREtaStretch) * dDbZs;
double dDxZ = (m_grid.GetZtop() - dZs) * dDxREtaStretch;
/*
double dDaZ = dbZ * dDaZs;
double dDbZ = dbZ * dDbZs;
double dDxZ = m_grid.GetZtop() - dZs * m_grid.GetZtop() *
cosh(m_grid.GetZtop() * (1.0 - dREtaStretch) / m_dSL) /
(m_dSL * sinh(m_grid.GetZtop() / m_dSL));
dDxZ *= dDxREtaStretch;
*/
// Calculate pointwise Jacobian
m_dataJacobian[k][iA][iB] =
dDxZ * m_dataJacobian2D[iA][iB];
// Element area associated with each model level GLL node
m_dataElementArea[k][iA][iB] =
m_dataJacobian[k][iA][iB]
* dWL[i] * GetElementDeltaA()
* dWL[j] * GetElementDeltaB()
* dWNode[k];
// Contravariant metric components
m_dataContraMetricA[k][iA][iB][0] =
m_dataContraMetric2DA[iA][iB][0];
m_dataContraMetricA[k][iA][iB][1] =
m_dataContraMetric2DA[iA][iB][1];
m_dataContraMetricA[k][iA][iB][2] =
- dDaZ / dDxZ;
m_dataContraMetricB[k][iA][iB][0] =
m_dataContraMetric2DB[iA][iB][0];
m_dataContraMetricB[k][iA][iB][1] =
m_dataContraMetric2DB[iA][iB][1];
m_dataContraMetricB[k][iA][iB][2] =
- dDbZ / dDxZ;
m_dataContraMetricXi[k][iA][iB][0] =
m_dataContraMetricA[k][iA][iB][2];
m_dataContraMetricXi[k][iA][iB][1] =
m_dataContraMetricB[k][iA][iB][2];
m_dataContraMetricXi[k][iA][iB][2] =
(1.0 + dDaZ * dDaZ + dDbZ * dDbZ) / (dDxZ * dDxZ);
// Covariant metric components
m_dataCovMetricA[k][iA][iB][0] =
m_dataCovMetric2DA[iA][iB][0] + dDaZ * dDaZ;
m_dataCovMetricA[k][iA][iB][1] =
m_dataCovMetric2DA[iA][iB][1] + dDaZ * dDbZ;
m_dataCovMetricA[k][iA][iB][2] =
dDaZ * dDxZ;
m_dataCovMetricB[k][iA][iB][0] =
m_dataCovMetric2DB[iA][iB][0] + dDbZ * dDaZ;
m_dataCovMetricB[k][iA][iB][1] =
m_dataCovMetric2DB[iA][iB][1] + dDbZ * dDbZ;
m_dataCovMetricB[k][iA][iB][2] =
dDbZ * dDxZ;
m_dataCovMetricXi[k][iA][iB][0] =
dDaZ * dDxZ;
m_dataCovMetricXi[k][iA][iB][1] =
dDbZ * dDxZ;
m_dataCovMetricXi[k][iA][iB][2] =
dDxZ * dDxZ;
// Derivatives of the vertical coordinate transform
m_dataDerivRNode[k][iA][iB][0] = dDaZ;
m_dataDerivRNode[k][iA][iB][1] = dDbZ;
m_dataDerivRNode[k][iA][iB][2] = dDxZ;
}
// Metric terms at vertical interfaces
for (int k = 0; k <= m_grid.GetRElements(); k++) {
// Gal-Chen and Somerville (1975) terrain following coord
// Schar Exponential decay terrain following coord
double dREta = m_grid.GetREtaInterface(k);
/*
double dREtaStretch;
double dDxREtaStretch;
m_grid.EvaluateVerticalStretchF(
dREta, dREtaStretch, dDxREtaStretch);
double dZ = dZs + (m_grid.GetZtop() - dZs) * dREtaStretch;
double dDaZ = (1.0 - dREtaStretch) * dDaZs;
double dDbZ = (1.0 - dREtaStretch) * dDbZs;
double dDxZ = (m_grid.GetZtop() - dZs) * dDxREtaStretch;
*/
double dREtaStretch;
double dDxREtaStretch;
m_grid.EvaluateVerticalStretchF(
dREta, dREtaStretch, dDxREtaStretch);
/*
//double dZ = dZs + (m_grid.GetZtop() - dZs) * dREtaStretch;
double dbZ = sinh(m_grid.GetZtop() * (1.0 - dREtaStretch) / m_dSL) /
sinh(m_grid.GetZtop() / m_dSL);
double dZ = m_grid.GetZtop() * dREtaStretch + dZs * dbZ;
*/
double dDaZ = (1.0 - dREtaStretch) * dDaZs;
double dDbZ = (1.0 - dREtaStretch) * dDbZs;
double dDxZ = (m_grid.GetZtop() - dZs) * dDxREtaStretch;
/*
double dDaZ = dbZ * dDaZs;
double dDbZ = dbZ * dDbZs;
double dDxZ = m_grid.GetZtop() - dZs * m_grid.GetZtop() *
cosh(m_grid.GetZtop() * (1.0 - dREtaStretch) / m_dSL) /
(m_dSL * sinh(m_grid.GetZtop() / m_dSL));
dDxZ *= dDxREtaStretch;
*/
// Calculate pointwise Jacobian
m_dataJacobianREdge[k][iA][iB] =
dDxZ * m_dataJacobian2D[iA][iB];
// Element area associated with each model interface GLL node
m_dataElementAreaREdge[k][iA][iB] =
m_dataJacobianREdge[k][iA][iB]
* dWL[i] * GetElementDeltaA()
* dWL[j] * GetElementDeltaB()
* dWREdge[k];
// Components of the contravariant metric
m_dataContraMetricAREdge[k][iA][iB][0] =
m_dataContraMetric2DA[iA][iB][0];
m_dataContraMetricAREdge[k][iA][iB][1] =
m_dataContraMetric2DA[iA][iB][1];
m_dataContraMetricAREdge[k][iA][iB][2] =
- dDaZ / dDxZ;
m_dataContraMetricBREdge[k][iA][iB][0] =
m_dataContraMetric2DB[iA][iB][0];
m_dataContraMetricBREdge[k][iA][iB][1] =
m_dataContraMetric2DB[iA][iB][1];
m_dataContraMetricBREdge[k][iA][iB][2] =
- dDbZ / dDxZ;
m_dataContraMetricXiREdge[k][iA][iB][0] =
- dDaZ / dDxZ;
m_dataContraMetricXiREdge[k][iA][iB][1] =
- dDbZ / dDxZ;
m_dataContraMetricXiREdge[k][iA][iB][2] =
(1.0 + dDaZ * dDaZ + dDbZ * dDbZ) / (dDxZ * dDxZ);
// Derivatives of the vertical coordinate transform
m_dataDerivRREdge[k][iA][iB][0] = dDaZ;
m_dataDerivRREdge[k][iA][iB][1] = dDbZ;
m_dataDerivRREdge[k][iA][iB][2] = dDxZ;
}
}
}
}
}
}
void GridPatchCSGLL::EvaluateGeometricTerms() {
// Physical constants
const PhysicalConstants & phys = m_grid.GetModel().GetPhysicalConstants();
// 2D equation set
bool fIs2DEquationSet = false;
if (m_grid.GetModel().GetEquationSet().GetDimensionality() == 2) {
fIs2DEquationSet = true;
}
if ((fIs2DEquationSet) && (m_grid.GetZtop() != 1.0)) {
_EXCEPTIONT("Ztop must be 1.0 for 2D equation sets");
}
// Obtain Gauss Lobatto quadrature nodes and weights
DataArray1D<double> dGL;
DataArray1D<double> dWL;
GaussLobattoQuadrature::GetPoints(m_nHorizontalOrder, 0.0, 1.0, dGL, dWL);
// Obtain normalized areas in the vertical
const DataArray1D<double> & dWNode =
m_grid.GetREtaLevelsNormArea();
const DataArray1D<double> & dWREdge =
m_grid.GetREtaInterfacesNormArea();
// Verify that normalized areas are correct
double dWNodeSum = 0.0;
for (int k = 0; k < dWNode.GetRows(); k++) {
dWNodeSum += dWNode[k];
}
if (fabs(dWNodeSum - 1.0) > 1.0e-13) {
_EXCEPTION1("Error in normalized areas (%1.15e)", dWNodeSum);
}
if (m_grid.GetVerticalStaggering() !=
Grid::VerticalStaggering_Interfaces
) {
double dWREdgeSum = 0.0;
for (int k = 0; k < dWREdge.GetRows(); k++) {
dWREdgeSum += dWREdge[k];
}
if (fabs(dWREdgeSum - 1.0) > 1.0e-13) {
_EXCEPTION1("Error in normalized areas (%1.15e)", dWREdgeSum);
}
}
// Derivatives of basis functions
GridCSGLL & gridCSGLL = dynamic_cast<GridCSGLL &>(m_grid);
const DataArray2D<double> & dDxBasis1D = gridCSGLL.GetDxBasis1D();
// Initialize the Coriolis force at each node
for (int i = 0; i < m_box.GetATotalWidth(); i++) {
for (int j = 0; j < m_box.GetBTotalWidth(); j++) {
m_dataCoriolisF[i][j] = 2.0 * phys.GetOmega() * sin(m_dataLat[i][j]);
}
}
// Initialize metric in terrain-following coords
for (int a = 0; a < GetElementCountA(); a++) {
for (int b = 0; b < GetElementCountB(); b++) {
for (int i = 0; i < m_nHorizontalOrder; i++) {
for (int j = 0; j < m_nHorizontalOrder; j++) {
// Nodal points
int iElementA = m_box.GetAInteriorBegin() + a * m_nHorizontalOrder;
int iElementB = m_box.GetBInteriorBegin() + b * m_nHorizontalOrder;
int iA = iElementA + i;
int iB = iElementB + j;
// Gnomonic coordinates
double dX = tan(m_dANode[iA]);
double dY = tan(m_dBNode[iB]);
double dDelta2 = (1.0 + dX * dX + dY * dY);
double dDelta = sqrt(dDelta2);
// Topography height and its derivatives
double dZs = m_dataTopography[iA][iB];
double dDaZs = m_dataTopographyDeriv[0][iA][iB];
double dDbZs = m_dataTopographyDeriv[1][iA][iB];
// 2D equations
if (fIs2DEquationSet) {
dZs = 0.0;
dDaZs = 0.0;
dDbZs = 0.0;
}
// Initialize 2D Jacobian
m_dataJacobian2D[iA][iB] =
(1.0 + dX * dX) * (1.0 + dY * dY) / (dDelta * dDelta * dDelta);
m_dataJacobian2D[iA][iB] *=
phys.GetEarthRadius()
* phys.GetEarthRadius();
// Initialize 2D contravariant metric
double dContraMetricScale =
dDelta2 / (1.0 + dX * dX) / (1.0 + dY * dY)
/ (phys.GetEarthRadius() * phys.GetEarthRadius());
m_dataContraMetric2DA[iA][iB][0] =
dContraMetricScale * (1.0 + dY * dY);
m_dataContraMetric2DA[iA][iB][1] =
dContraMetricScale * dX * dY;
m_dataContraMetric2DB[iA][iB][0] =
dContraMetricScale * dX * dY;
m_dataContraMetric2DB[iA][iB][1] =
dContraMetricScale * (1.0 + dX * dX);
// Initialize 2D covariant metric
double dCovMetricScale =
phys.GetEarthRadius() * phys.GetEarthRadius()
* (1.0 + dX * dX) * (1.0 + dY * dY)
/ (dDelta2 * dDelta2);
m_dataCovMetric2DA[iA][iB][0] =
dCovMetricScale * (1.0 + dX * dX);
m_dataCovMetric2DA[iA][iB][1] =
dCovMetricScale * (- dX * dY);
m_dataCovMetric2DB[iA][iB][0] =
dCovMetricScale * (- dX * dY);
m_dataCovMetric2DB[iA][iB][1] =
dCovMetricScale * (1.0 + dY * dY);
// Vertical coordinate transform and its derivatives
for (int k = 0; k < m_grid.GetRElements(); k++) {
// Gal-Chen and Somerville (1975) linear terrain-following coord
double dREta = m_grid.GetREtaLevel(k);
/*
double dREtaStretch;
double dDxREtaStretch;
m_grid.EvaluateVerticalStretchF(
dREta, dREtaStretch, dDxREtaStretch);
double dZ = dZs + (m_grid.GetZtop() - dZs) * dREtaStretch;
double dDaR = (1.0 - dREtaStretch) * dDaZs;
double dDbR = (1.0 - dREtaStretch) * dDbZs;
double dDxR = (m_grid.GetZtop() - dZs) * dDxREtaStretch;
*/
double dZ = dZs + (m_grid.GetZtop() - dZs) * dREta;
double dDaR = (1.0 - dREta) * dDaZs;
double dDbR = (1.0 - dREta) * dDbZs;
double dDxR = (m_grid.GetZtop() - dZs);
// Calculate pointwise Jacobian
m_dataJacobian[k][iA][iB] = dDxR * m_dataJacobian2D[iA][iB];
// Element area associated with each model level GLL node
m_dataElementAreaNode[k][iA][iB] =
m_dataJacobian[k][iA][iB]
* dWL[i] * GetElementDeltaA()
* dWL[j] * GetElementDeltaB()
* dWNode[k];
// Contravariant metric components
m_dataContraMetricA[k][iA][iB][0] =
m_dataContraMetric2DA[iA][iB][0];
m_dataContraMetricA[k][iA][iB][1] =
m_dataContraMetric2DA[iA][iB][1];
m_dataContraMetricA[k][iA][iB][2] =
- dContraMetricScale / dDxR * (
(1.0 + dY * dY) * dDaR + dX * dY * dDbR);
m_dataContraMetricB[k][iA][iB][0] =
m_dataContraMetric2DB[iA][iB][0];
m_dataContraMetricB[k][iA][iB][1] =
m_dataContraMetric2DB[iA][iB][1];
m_dataContraMetricB[k][iA][iB][2] =
- dContraMetricScale / dDxR * (
dX * dY * dDaR + (1.0 + dX * dX) * dDbR);
m_dataContraMetricXi[k][iA][iB][0] =
m_dataContraMetricA[k][iA][iB][2];
m_dataContraMetricXi[k][iA][iB][1] =
m_dataContraMetricB[k][iA][iB][2];
m_dataContraMetricXi[k][iA][iB][2] =
1.0 / (dDxR * dDxR)
- 1.0 / dDxR * (
m_dataContraMetricXi[k][iA][iB][0] * dDaR
+ m_dataContraMetricXi[k][iA][iB][1] * dDbR);
// Derivatives of the vertical coordinate transform
m_dataDerivRNode[k][iA][iB][0] = dDaR;
m_dataDerivRNode[k][iA][iB][1] = dDbR;
m_dataDerivRNode[k][iA][iB][2] = dDxR;
}
// Metric terms at vertical interfaces
for (int k = 0; k <= m_grid.GetRElements(); k++) {
// Gal-Chen and Somerville (1975) linear terrain-following coord
double dREta = m_grid.GetREtaInterface(k);
/*
double dREtaStretch;
double dDxREtaStretch;
m_grid.EvaluateVerticalStretchF(
dREta, dREtaStretch, dDxREtaStretch);
double dZ = dZs + (m_grid.GetZtop() - dZs) * dREtaStretch;
double dDaR = (1.0 - dREtaStretch) * dDaZs;
double dDbR = (1.0 - dREtaStretch) * dDbZs;
double dDxR = (m_grid.GetZtop() - dZs) * dDxREtaStretch;
*/
double dZ = dZs + (m_grid.GetZtop() - dZs) * dREta;
double dDaR = (1.0 - dREta) * dDaZs;
double dDbR = (1.0 - dREta) * dDbZs;
double dDxR = (m_grid.GetZtop() - dZs);
// Calculate pointwise Jacobian
m_dataJacobianREdge[k][iA][iB] =
(1.0 + dX * dX) * (1.0 + dY * dY) / (dDelta * dDelta * dDelta);
m_dataJacobianREdge[k][iA][iB] *=
dDxR
* phys.GetEarthRadius()
* phys.GetEarthRadius();
// Element area associated with each model interface GLL node
m_dataElementAreaREdge[k][iA][iB] =
m_dataJacobianREdge[k][iA][iB]
* dWL[i] * GetElementDeltaA()
* dWL[j] * GetElementDeltaB()
* dWREdge[k];
// Contravariant metric (alpha)
m_dataContraMetricAREdge[k][iA][iB][0] =
m_dataContraMetric2DA[iA][iB][0];
m_dataContraMetricAREdge[k][iA][iB][1] =
m_dataContraMetric2DA[iA][iB][1];
m_dataContraMetricAREdge[k][iA][iB][2] =
- dContraMetricScale / dDxR * (
(1.0 + dY * dY) * dDaR + dX * dY * dDbR);
// Contravariant metric (beta)
m_dataContraMetricBREdge[k][iA][iB][0] =
m_dataContraMetric2DB[iA][iB][0];
m_dataContraMetricBREdge[k][iA][iB][1] =
m_dataContraMetric2DB[iA][iB][1];
m_dataContraMetricBREdge[k][iA][iB][2] =
- dContraMetricScale / dDxR * (
dX * dY * dDaR + (1.0 + dX * dX) * dDbR);
// Contravariant metric (xi)
m_dataContraMetricXiREdge[k][iA][iB][0] =
- dContraMetricScale / dDxR * (
(1.0 + dY * dY) * dDaR + dX * dY * dDbR);
m_dataContraMetricXiREdge[k][iA][iB][1] =
- dContraMetricScale / dDxR * (
dX * dY * dDaR + (1.0 + dX * dX) * dDbR);
m_dataContraMetricXiREdge[k][iA][iB][2] =
1.0 / (dDxR * dDxR)
- 1.0 / dDxR * (
m_dataContraMetricXiREdge[k][iA][iB][0] * dDaR
+ m_dataContraMetricXiREdge[k][iA][iB][1] * dDbR);
// Derivatives of the vertical coordinate transform
m_dataDerivRREdge[k][iA][iB][0] = dDaR;
m_dataDerivRREdge[k][iA][iB][1] = dDbR;
m_dataDerivRREdge[k][iA][iB][2] = dDxR;
}
}
}
}
}
}
void GridPatchCartesianGLL::EvaluateTopography(
const TestCase & test
) {
const PhysicalConstants & phys = m_grid.GetModel().GetPhysicalConstants();
// Compute values of topography
for (int i = 0; i < m_box.GetATotalWidth(); i++) {
for (int j = 0; j < m_box.GetBTotalWidth(); j++) {
double dX = m_box.GetANode(i);
double dY = m_box.GetBNode(j);
m_dataTopography[i][j] = test.EvaluateTopography(phys, dX, dY);
if (m_dataTopography[i][j] >= m_grid.GetZtop()) {
_EXCEPTIONT("TestCase topography exceeds model top.");
}
}
}
// Get derivatves from basis
GridCartesianGLL & gridCartesianGLL =
dynamic_cast<GridCartesianGLL &>(m_grid);
const DataMatrix<double> & dDxBasis1D =
gridCartesianGLL.GetDxBasis1D();
// Compute derivatives of topography
for (int a = 0; a < GetElementCountA(); a++) {
for (int b = 0; b < GetElementCountB(); b++) {
for (int i = 0; i < m_nHorizontalOrder; i++) {
for (int j = 0; j < m_nHorizontalOrder; j++) {
// Nodal points
int iElementA = m_box.GetAInteriorBegin() + a * m_nHorizontalOrder;
int iElementB = m_box.GetBInteriorBegin() + b * m_nHorizontalOrder;
int iA = iElementA + i;
int iB = iElementB + j;
// Topography height and its derivatives
double dZs = m_dataTopography[iA][iB];
double dDaZs = 0.0;
double dDbZs = 0.0;
for (int s = 0; s < m_nHorizontalOrder; s++) {
dDaZs += dDxBasis1D[s][i] * m_dataTopography[iElementA+s][iB];
dDbZs += dDxBasis1D[s][j] * m_dataTopography[iA][iElementB+s];
}
dDaZs /= GetElementDeltaA();
dDbZs /= GetElementDeltaB();
m_dataTopographyDeriv[0][iA][iB] = dDaZs;
m_dataTopographyDeriv[1][iA][iB] = dDbZs;
}
}
}
}
}
void GridPatchCSGLL::EvaluateTopography(
const TestCase & test
) {
const PhysicalConstants & phys = m_grid.GetModel().GetPhysicalConstants();
// Compute values of topography
for (int i = 0; i < m_box.GetATotalWidth(); i++) {
for (int j = 0; j < m_box.GetBTotalWidth(); j++) {
double dLon;
double dLat;
CubedSphereTrans::RLLFromABP(
m_dANode[i],
m_dBNode[j],
m_box.GetPanel(),
dLon,
dLat);
m_dataTopography[i][j] = test.EvaluateTopography(phys, dLon, dLat);
}
}
// Get derivatves from basis
GridCSGLL & gridCSGLL = dynamic_cast<GridCSGLL &>(m_grid);
const DataArray2D<double> & dDxBasis1D = gridCSGLL.GetDxBasis1D();
// Compute derivatives of topography
for (int a = 0; a < GetElementCountA(); a++) {
for (int b = 0; b < GetElementCountB(); b++) {
for (int i = 0; i < m_nHorizontalOrder; i++) {
for (int j = 0; j < m_nHorizontalOrder; j++) {
// Nodal points
int iElementA = m_box.GetAInteriorBegin() + a * m_nHorizontalOrder;
int iElementB = m_box.GetBInteriorBegin() + b * m_nHorizontalOrder;
int iA = iElementA + i;
int iB = iElementB + j;
// Topography height and its derivatives
double dZs = m_dataTopography[iA][iB];
double dDaZs = 0.0;
double dDbZs = 0.0;
for (int s = 0; s < m_nHorizontalOrder; s++) {
dDaZs += dDxBasis1D[s][i] * m_dataTopography[iElementA+s][iB];
dDbZs += dDxBasis1D[s][j] * m_dataTopography[iA][iElementB+s];
}
dDaZs /= GetElementDeltaA();
dDbZs /= GetElementDeltaB();
m_dataTopographyDeriv[0][iA][iB] = dDaZs;
m_dataTopographyDeriv[1][iA][iB] = dDbZs;
}
}
}
}
}
