void TimestepSchemeARS222::Step(
bool fFirstStep,
bool fLastStep,
const Time & time,
double dDeltaT
) {
// Get a copy of the grid
Grid * pGrid = m_model.GetGrid();
// Get a copy of the HorizontalDynamics
HorizontalDynamics * pHorizontalDynamics = m_model.GetHorizontalDynamics();
// Get a copy of the VerticalDynamics
VerticalDynamics * pVerticalDynamics = m_model.GetVerticalDynamics();
// u2 explicit evaluation combination
m_du2fCombo[0] = 1.0 - m_dExpCf[1][0] / m_dExpCf[0][0];
m_du2fCombo[1] = m_dExpCf[1][0] / m_dExpCf[0][0] -
m_dImpCf[1][0] / m_dImpCf[0][0];
m_du2fCombo[2] = m_dImpCf[1][0] / m_dImpCf[0][0];
m_du2fCombo[3] = 0.0;
//std::cout << "Entering substages at the timestep... \n";
// STAGE 1
// Compute uf1 into index 1
pGrid->CopyData(0, 1, DataType_State);
pGrid->CopyData(0, 1, DataType_Tracers);
pHorizontalDynamics->StepExplicit(
0, 1, time, m_dExpCf[0][0] * dDeltaT);
pVerticalDynamics->StepExplicit(
0, 1, time, m_dExpCf[0][0] * dDeltaT);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Compute u1 into index 2
pGrid->CopyData(1, 2, DataType_State);
pGrid->CopyData(1, 2, DataType_State);
pVerticalDynamics->StepImplicit(
2, 2, time, m_dImpCf[0][0] * dDeltaT);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// STAGE 2
// Compute uf2 from u1 (index 2) into index 3
pGrid->LinearCombineData(m_du2fCombo, 3, DataType_State);
pGrid->LinearCombineData(m_du2fCombo, 3, DataType_Tracers);
pHorizontalDynamics->StepExplicit(
2, 3, time, m_dExpCf[1][1] * dDeltaT);
pVerticalDynamics->StepExplicit(
2, 3, time, m_dExpCf[1][1] * dDeltaT);
pGrid->PostProcessSubstage(3, DataType_State);
pGrid->PostProcessSubstage(3, DataType_Tracers);
// Compute u2 from uf2 (index 3) into index 2
pVerticalDynamics->StepImplicit(
3, 3, time, m_dImpCf[1][1] * dDeltaT);
pGrid->PostProcessSubstage(3, DataType_State);
pGrid->PostProcessSubstage(3, DataType_Tracers);
// Apply hyperdiffusion at the end of the explicit substep (ask Paul)
pGrid->CopyData(3, 2, DataType_State);
pGrid->CopyData(3, 2, DataType_Tracers);
pHorizontalDynamics->StepAfterSubCycle(2, 1, 3, time, dDeltaT);
pGrid->CopyData(1, 0, DataType_State);
pGrid->CopyData(1, 0, DataType_Tracers);
}
void TimestepSchemeSSP3332::Step(
bool fFirstStep,
bool fLastStep,
const Time & time,
double dDeltaT
) {
// Get a copy of the grid
Grid * pGrid = m_model.GetGrid();
// Get a copy of the HorizontalDynamics
HorizontalDynamics * pHorizontalDynamics = m_model.GetHorizontalDynamics();
// Get a copy of the VerticalDynamics
VerticalDynamics * pVerticalDynamics = m_model.GetVerticalDynamics();
// u2 explicit evaluation combination
m_du2fCombo[0] = 1.0 - m_dImpCf[1][0] / m_dImpCf[0][0];
m_du2fCombo[1] = 0.0;
m_du2fCombo[2] = m_dImpCf[1][0] / m_dImpCf[0][0];
m_du2fCombo[3] = 0.0;
m_du2fCombo[4] = 0.0;
m_du2fCombo[5] = 0.0;
m_du2fCombo[6] = 0.0;
m_du2fCombo[7] = 0.0;
// u3 explicit evaluation combination
m_du3fCombo[0] = 1.0 + m_dImpCf[1][0] / m_dImpCf[0][0] *
m_dExpCf[2][0] / m_dExpCf[1][0] -
m_dExpCf[2][0] / m_dExpCf[1][0] -
m_dImpCf[2][0] / m_dImpCf[0][0];
m_du3fCombo[1] = 0.0;
m_du3fCombo[2] = m_dImpCf[2][0] / m_dImpCf[0][0] -
m_dImpCf[1][0] / m_dImpCf[0][0] *
m_dExpCf[2][0] / m_dExpCf[1][0];
m_du3fCombo[3] = m_dExpCf[2][0] / m_dExpCf[1][0];
m_du3fCombo[4] = 0.0;
m_du3fCombo[5] = 0.0;
m_du3fCombo[6] = 0.0;
m_du3fCombo[7] = 0.0;
m_du3fCombo[8] = 0.0;
// u4 explicit evaluation combination
m_du4fCombo[0] = 1.0 - m_dExpCf[3][0] / m_dImpCf[0][0];
m_du4fCombo[1] = 0.0;
m_du4fCombo[2] = m_dImpCf[3][0] / m_dImpCf[0][0];
m_du4fCombo[3] = m_dExpCf[3][0] / m_dExpCf[1][0] -
m_dImpCf[3][1] / m_dImpCf[1][1];
m_du4fCombo[4] = m_dImpCf[3][1] / m_dImpCf[1][1];
m_du4fCombo[5] = m_dExpCf[3][1] / m_dExpCf[2][1] -
m_dImpCf[3][2] / m_dImpCf[2][2];
m_du4fCombo[6] = m_dImpCf[3][2] / m_dImpCf[2][2];
m_du4fCombo[7] = -m_dExpCf[3][0] / m_dExpCf[1][0];
m_du4fCombo[8] = -m_dExpCf[3][1] / m_dExpCf[2][1];
// STAGE 1
// Compute u1 into index 2
pGrid->CopyData(0, 2, DataType_State);
pGrid->CopyData(0, 2, DataType_State);
pVerticalDynamics->StepImplicit(
2, 2, time, m_dImpCf[0][0] * dDeltaT);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// STAGE 2
// Compute uf1 from u0 (index 2) into index 7
pGrid->LinearCombineData(m_du2fCombo, 7, DataType_State);
pGrid->LinearCombineData(m_du2fCombo, 7, DataType_Tracers);
pGrid->CopyData(7, 3, DataType_State);
pGrid->CopyData(7, 3, DataType_Tracers);
pHorizontalDynamics->StepExplicit(
2, 3, time, m_dExpCf[1][0] * dDeltaT);
pVerticalDynamics->StepExplicit(
2, 3, time, m_dExpCf[1][0] * dDeltaT);
pGrid->PostProcessSubstage(3, DataType_State);
pGrid->PostProcessSubstage(3, DataType_Tracers);
// Compute u2 from uf2 (index 3) into index 4
pGrid->CopyData(3, 4, DataType_State);
pGrid->CopyData(3, 4, DataType_State);
pVerticalDynamics->StepImplicit(
4, 4, time, m_dImpCf[1][1] * dDeltaT);
pGrid->PostProcessSubstage(4, DataType_State);
pGrid->PostProcessSubstage(4, DataType_Tracers);
// STAGE 3
// Compute uf3 from u2 (index 4) into index 8
pGrid->LinearCombineData(m_du3fCombo, 8, DataType_State);
pGrid->LinearCombineData(m_du3fCombo, 8, DataType_Tracers);
pGrid->CopyData(8, 5, DataType_State);
pGrid->CopyData(8, 5, DataType_Tracers);
pHorizontalDynamics->StepExplicit(
4, 5, time, m_dExpCf[2][1] * dDeltaT);
pVerticalDynamics->StepExplicit(
4, 5, time, m_dExpCf[2][1] * dDeltaT);
pGrid->PostProcessSubstage(5, DataType_State);
pGrid->PostProcessSubstage(5, DataType_Tracers);
// Compute u3 from uf3 (index 3) into index 6
pGrid->CopyData(5, 6, DataType_State);
pGrid->CopyData(5, 6, DataType_State);
pVerticalDynamics->StepImplicit(
6, 6, time, m_dImpCf[2][2] * dDeltaT);
pGrid->PostProcessSubstage(6, DataType_State);
pGrid->PostProcessSubstage(6, DataType_Tracers);
// STAGE 4
// Compute uf4 from u3 (index 6) into index 9
pGrid->LinearCombineData(m_du4fCombo, 1, DataType_State);
pGrid->LinearCombineData(m_du4fCombo, 1, DataType_Tracers);
pHorizontalDynamics->StepExplicit(
6, 1, time, m_dExpCf[3][2] * dDeltaT);
pVerticalDynamics->StepExplicit(
6, 1, time, m_dExpCf[3][2] * dDeltaT);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// NO IMPLICIT STEP ON THE LAST STAGE
// Apply hyperdiffusion at the end of the explicit substep (ask Paul)
pGrid->CopyData(1, 2, DataType_State);
pGrid->CopyData(1, 2, DataType_Tracers);
pHorizontalDynamics->StepAfterSubCycle(2, 1, 3, time, dDeltaT);
pGrid->CopyData(1, 0, DataType_State);
pGrid->CopyData(1, 0, DataType_Tracers);
}
void TimestepSchemeARK4::Step(
bool fFirstStep,
bool fLastStep,
const Time & time,
double dDeltaT
) {
// Get a copy of the grid
Grid * pGrid = m_model.GetGrid();
// Get a copy of the HorizontalDynamics
HorizontalDynamics * pHorizontalDynamics = m_model.GetHorizontalDynamics();
// Get a copy of the VerticalDynamics
VerticalDynamics * pVerticalDynamics = m_model.GetVerticalDynamics();
// K0 combination
m_dK0Combo[0] = -1.0 / (dDeltaT * m_dImpCf[0][0]);;
m_dK0Combo[1] = 1.0 / (dDeltaT * m_dImpCf[0][0]);;
m_dK0Combo[2] = 0.0;
m_dK0Combo[3] = 0.0;
// u1 implicit evaluation combination
m_du1fCombo[0] = 1.0;
m_du1fCombo[1] = 0.0;
m_du1fCombo[2] = 0.0;
m_du1fCombo[3] = dDeltaT * m_dImpCf[1][0];
// Kh1 combination
m_dKh1Combo[0] = -1.0 / (dDeltaT * m_dExpCf[1][0]);
m_dKh1Combo[1] = 1.0 / (dDeltaT * m_dExpCf[1][0]);
m_dKh1Combo[2] = 0.0;
m_dKh1Combo[3] = -m_dImpCf[0][0] / m_dExpCf[1][0];
m_dKh1Combo[4] = 0.0;
// K1 combination
m_dK1Combo[0] = -1.0 / (dDeltaT * m_dImpCf[1][1]);
m_dK1Combo[1] = 0.0;
m_dK1Combo[2] = 1.0 / (dDeltaT * m_dImpCf[1][1]);
m_dK1Combo[3] = -m_dImpCf[0][0] / m_dImpCf[1][1];
m_dK1Combo[4] = -m_dExpCf[1][0] / m_dImpCf[1][1];
m_dK1Combo[5] = 0.0;
// u2 implicit evaluation combination
m_du2fCombo[0] = 1.0;
m_du2fCombo[1] = 0.0;
m_du2fCombo[2] = 0.0;
m_du2fCombo[3] = dDeltaT * m_dImpCf[2][0];
m_du2fCombo[4] = dDeltaT * m_dExpCf[2][0];
m_du2fCombo[5] = dDeltaT * m_dImpCf[2][1];
// K2 combination
m_dK2Combo[0] = -1.0 / (dDeltaT * m_dImpCf[2][2]);
m_dK2Combo[1] = 0.0;
m_dK2Combo[2] = 1.0 / (dDeltaT * m_dImpCf[2][2]);
m_dK2Combo[3] = -m_dImpCf[1][0] / m_dImpCf[2][2];
m_dK2Combo[4] = -m_dExpCf[2][0] / m_dImpCf[2][2];
m_dK2Combo[5] = -m_dImpCf[2][1] / m_dImpCf[2][2];
m_dK2Combo[6] = -m_dExpCf[2][1] / m_dImpCf[2][2];
m_dK2Combo[7] = 0.0;
// Kh2 combination
m_dKh2Combo[0] = -1.0 / (dDeltaT * m_dExpCf[2][1]);
m_dKh2Combo[1] = 1.0 / (dDeltaT * m_dExpCf[2][1]);
m_dKh2Combo[2] = 0.0;
m_dKh2Combo[3] = -m_dImpCf[2][0] / m_dExpCf[2][1];
m_dKh2Combo[4] = -m_dExpCf[2][0] / m_dExpCf[2][1];
m_dKh2Combo[5] = -m_dImpCf[2][1] / m_dExpCf[2][1];
m_dKh2Combo[6] = 0.0;
// u3 implicit evaluation combination
m_du3fCombo[0] = 1.0;
m_du3fCombo[1] = 0.0;
m_du3fCombo[2] = 0.0;
m_du3fCombo[3] = dDeltaT * m_dImpCf[3][0];
m_du3fCombo[4] = dDeltaT * m_dExpCf[3][0];
m_du3fCombo[5] = dDeltaT * m_dImpCf[3][1];
m_du3fCombo[6] = dDeltaT * m_dExpCf[3][1];
m_du3fCombo[7] = dDeltaT * m_dImpCf[3][2];
// K3 combination
m_dK3Combo[0] = -1.0 / (dDeltaT * m_dImpCf[3][3]);
m_dK3Combo[1] = 0.0;
m_dK3Combo[2] = 1.0 / (dDeltaT * m_dImpCf[3][3]);
m_dK3Combo[3] = -m_dImpCf[3][0] / m_dImpCf[3][3];
m_dK3Combo[4] = -m_dExpCf[3][0] / m_dImpCf[3][3];
m_dK3Combo[5] = -m_dImpCf[3][1] / m_dImpCf[3][3];
m_dK3Combo[6] = -m_dExpCf[3][1] / m_dImpCf[3][3];
m_dK3Combo[7] = -m_dImpCf[3][2] / m_dImpCf[3][3];
m_dK3Combo[8] = -m_dExpCf[3][2] / m_dImpCf[3][3];
m_dK3Combo[9] = 0.0;
// Kh3 combination
m_dKh3Combo[0] = -1.0 / (dDeltaT * m_dExpCf[3][2]);
m_dKh3Combo[1] = 1.0 / (dDeltaT * m_dExpCf[3][2]);
m_dKh3Combo[2] = 0.0;
m_dKh3Combo[3] = -m_dImpCf[3][0] / m_dExpCf[3][2];
m_dKh3Combo[4] = -m_dExpCf[3][0] / m_dExpCf[3][2];
m_dKh3Combo[5] = -m_dImpCf[3][1] / m_dExpCf[3][2];
m_dKh3Combo[6] = -m_dExpCf[3][1] / m_dExpCf[3][2];
m_dKh3Combo[7] = -m_dImpCf[3][2] / m_dExpCf[3][2];
m_dKh3Combo[8] = 0.0;
// uf4 explicit evaluation combination
m_du4fCombo[0] = 1.0;
m_du4fCombo[1] = 0.0;
m_du4fCombo[2] = 0.0;
m_du4fCombo[3] = dDeltaT * m_dImpCf[4][0];
m_du4fCombo[4] = dDeltaT * m_dExpCf[4][0];
m_du4fCombo[5] = dDeltaT * m_dImpCf[4][1];
m_du4fCombo[6] = dDeltaT * m_dExpCf[4][1];
m_du4fCombo[7] = dDeltaT * m_dImpCf[4][2];
m_du4fCombo[8] = dDeltaT * m_dExpCf[4][2];
m_du4fCombo[9] = dDeltaT * m_dImpCf[4][3];
// K4 combination
m_dK4Combo[0] = -1.0 / (dDeltaT * m_dImpCf[4][4]);
m_dK4Combo[1] = 0.0;
m_dK4Combo[2] = 1.0 / (dDeltaT * m_dImpCf[4][4]);
m_dK4Combo[3] = -m_dImpCf[4][0] / m_dImpCf[4][4];
m_dK4Combo[4] = -m_dExpCf[4][0] / m_dImpCf[4][4];
m_dK4Combo[5] = -m_dImpCf[4][1] / m_dImpCf[4][4];
m_dK4Combo[6] = -m_dExpCf[4][1] / m_dImpCf[4][4];
m_dK4Combo[7] = -m_dImpCf[4][2] / m_dImpCf[4][4];
m_dK4Combo[8] = -m_dExpCf[4][2] / m_dImpCf[4][4];
m_dK4Combo[9] = -m_dImpCf[4][3] / m_dImpCf[4][4];
m_dK4Combo[10] = -m_dExpCf[4][3] / m_dImpCf[4][4];
m_dK4Combo[11] = 0.0;
// Kh4 combination
m_dKh4Combo[0] = -1.0 / (dDeltaT * m_dExpCf[4][3]);
m_dKh4Combo[1] = 1.0 / (dDeltaT * m_dExpCf[4][3]);
m_dKh4Combo[2] = 0.0;
m_dKh4Combo[3] = -m_dImpCf[4][0] / m_dExpCf[4][3];
m_dKh4Combo[4] = -m_dExpCf[4][0] / m_dExpCf[4][3];
m_dKh4Combo[5] = -m_dImpCf[4][1] / m_dExpCf[4][3];
m_dKh4Combo[6] = -m_dExpCf[4][1] / m_dExpCf[4][3];
m_dKh4Combo[7] = -m_dImpCf[4][2] / m_dExpCf[4][3];
m_dKh4Combo[8] = -m_dExpCf[4][2] / m_dExpCf[4][3];
m_dKh4Combo[9] = -m_dImpCf[4][3] / m_dExpCf[4][3];
m_dKh4Combo[10] = 0.0;
// uf5 explicit evaluation combination
m_du5fCombo[0] = 1.0;
m_du5fCombo[1] = 0.0;
m_du5fCombo[2] = 0.0;
m_du5fCombo[3] = dDeltaT * m_dImpCf[5][0];
m_du5fCombo[4] = dDeltaT * m_dExpCf[5][0];
m_du5fCombo[5] = dDeltaT * m_dImpCf[5][1];
m_du5fCombo[6] = dDeltaT * m_dExpCf[5][1];
m_du5fCombo[7] = dDeltaT * m_dImpCf[5][2];
m_du5fCombo[8] = dDeltaT * m_dExpCf[5][2];
m_du5fCombo[9] = dDeltaT * m_dImpCf[5][3];
m_du5fCombo[10] = dDeltaT * m_dExpCf[5][3];
m_du5fCombo[11] = dDeltaT * m_dImpCf[5][4];
// K5 combination
m_dK5Combo[0] = -1.0 / (dDeltaT * m_dImpCf[5][5]);
m_dK5Combo[1] = 0.0;
m_dK5Combo[2] = 1.0 / (dDeltaT * m_dImpCf[5][5]);
m_dK5Combo[3] = -m_dImpCf[5][0] / m_dImpCf[5][5];
m_dK5Combo[4] = -m_dExpCf[5][0] / m_dImpCf[5][5];
m_dK5Combo[5] = -m_dImpCf[5][1] / m_dImpCf[5][5];
m_dK5Combo[6] = -m_dExpCf[5][1] / m_dImpCf[5][5];
m_dK5Combo[7] = -m_dImpCf[5][2] / m_dImpCf[5][5];
m_dK5Combo[8] = -m_dExpCf[5][2] / m_dImpCf[5][5];
m_dK5Combo[9] = -m_dImpCf[5][3] / m_dImpCf[5][5];
m_dK5Combo[10] = -m_dExpCf[5][3] / m_dImpCf[5][5];
m_dK5Combo[11] = -m_dImpCf[5][4] / m_dImpCf[5][5];
m_dK5Combo[12] = -m_dExpCf[5][4] / m_dImpCf[5][5];
m_dK5Combo[13] = 0.0;
// Kh5 combination
m_dKh5Combo[0] = -1.0 / (dDeltaT * m_dExpCf[5][4]);
m_dKh5Combo[1] = 1.0 / (dDeltaT * m_dExpCf[5][4]);
m_dKh5Combo[2] = 0.0;
m_dKh5Combo[3] = -m_dImpCf[5][0] / m_dExpCf[5][4];
m_dKh5Combo[4] = -m_dExpCf[5][0] / m_dExpCf[5][4];
m_dKh5Combo[5] = -m_dImpCf[5][1] / m_dExpCf[5][4];
m_dKh5Combo[6] = -m_dExpCf[5][1] / m_dExpCf[5][4];
m_dKh5Combo[7] = -m_dImpCf[5][2] / m_dExpCf[5][4];
m_dKh5Combo[8] = -m_dExpCf[5][2] / m_dExpCf[5][4];
m_dKh5Combo[9] = -m_dImpCf[5][3] / m_dExpCf[5][4];
m_dKh5Combo[10] = -m_dExpCf[5][3] / m_dExpCf[5][4];
m_dKh5Combo[11] = -m_dImpCf[5][4] / m_dExpCf[5][4];
m_dKh5Combo[12] = 0.0;
// uf6 explicit evaluation combination
m_du6fCombo[0] = 1.0;
m_du6fCombo[1] = 0.0;
m_du6fCombo[2] = 0.0;
m_du6fCombo[3] = dDeltaT * m_dImpCf[6][0];
m_du6fCombo[4] = dDeltaT * m_dExpCf[6][0];
m_du6fCombo[5] = dDeltaT * m_dImpCf[6][1];
m_du6fCombo[6] = dDeltaT * m_dExpCf[6][1];
m_du6fCombo[7] = dDeltaT * m_dImpCf[6][2];
m_du6fCombo[8] = dDeltaT * m_dExpCf[6][2];
m_du6fCombo[9] = dDeltaT * m_dImpCf[6][3];
m_du6fCombo[10] = dDeltaT * m_dExpCf[6][3];
m_du6fCombo[11] = dDeltaT * m_dImpCf[6][4];
m_du6fCombo[12] = dDeltaT * m_dExpCf[6][4];
m_du6fCombo[13] = dDeltaT * m_dImpCf[6][5];
// PRE-STAGE 1 - Implicit solve to start
Time timeSub0 = time;
double dtSub0 = m_dImpCf[0][0] * dDeltaT;
pGrid->CopyData(0, 1, DataType_State);
pHorizontalDynamics->StepImplicit(0, 1, timeSub0, dtSub0);
pVerticalDynamics->StepImplicit(0, 1, timeSub0, dtSub0);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Store the evaluation K1 to index 3
pGrid->LinearCombineData(m_dK0Combo, 3, DataType_State);
// SUBSTAGE 1
// Compute the explicit step to index 1
Time timeSub1 = time;
double dtSub1 = m_dExpCf[1][0] * dDeltaT;
pGrid->LinearCombineData(m_du1fCombo, 1, DataType_State);
pHorizontalDynamics->StepExplicit(0, 1, timeSub1, dtSub1);
pVerticalDynamics->StepExplicit(0, 1, timeSub1, dtSub1);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Store the evaluation Kh1 to index 4
pGrid->LinearCombineData(m_dKh1Combo, 4, DataType_State);
// Compute implicit step based on known data to index 2
pGrid->CopyData(1, 2, DataType_State);
dtSub1 = m_dImpCf[1][1] * dDeltaT;
pVerticalDynamics->StepImplicit(1, 2, timeSub1, dtSub1);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// Store the evaluation K1 to index 3
pGrid->LinearCombineData(m_dK1Combo, 5, DataType_State);
//std::cout << "Substage 1 done ... \n";
// SUBSTAGE 2
// Compute uf2
Time timeSub2 = time;
double dtSub2 = m_dExpCf[2][1] * dDeltaT;
pGrid->LinearCombineData(m_du2fCombo, 1, DataType_State);
pHorizontalDynamics->StepExplicit(2, 1, timeSub2, dtSub2);
pVerticalDynamics->StepExplicit(2, 1, timeSub2, dtSub2);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Store the evaluation Kh2 to index 6
pGrid->LinearCombineData(m_dKh2Combo, 6, DataType_State);
// Compute u2 from uf2 and store it to index 2 (over u1)
dtSub2 = m_dImpCf[2][2] * dDeltaT;
pGrid->CopyData(1, 2, DataType_State);
pVerticalDynamics->StepImplicit(1, 2, timeSub2, dtSub2);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// Store the evaluation K2 to index 7
pGrid->LinearCombineData(m_dK2Combo, 7, DataType_State);
//std::cout << "Substage 2 done ... \n";
// SUBSTAGE 3
// Compute uf3
Time timeSub3 = time;
double dtSub3 = m_dExpCf[3][2] * dDeltaT;
pGrid->LinearCombineData(m_du3fCombo, 1, DataType_State);
pHorizontalDynamics->StepExplicit(2, 1, timeSub2, dtSub2);
pVerticalDynamics->StepExplicit(2, 1, timeSub2, dtSub2);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Store the evaluation Kh3 to index 8
pGrid->LinearCombineData(m_dKh3Combo, 8, DataType_State);
// Compute u3 from uf3 and store it to index 2 (over u2)
dtSub3 = m_dImpCf[3][3] * dDeltaT;
pGrid->CopyData(1, 2, DataType_State);
pVerticalDynamics->StepImplicit(1, 2, timeSub3, dtSub3);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// Store the evaluation K3 to index 9
pGrid->LinearCombineData(m_dK3Combo, 9, DataType_State);
//std::cout << "Substage 3 done ... \n";
// SUBSTAGE 4 - MODIFIED DUE TO EXPLICIT ZERO EVALUATION
// Compute uf4 from u3 and store it to index 2
Time timeSub4 = time;
double dtSub4 = m_dExpCf[4][3] * dDeltaT;
pGrid->LinearCombineData(m_du4fCombo, 1, DataType_State);
pHorizontalDynamics->StepExplicit(2, 1, timeSub4, dtSub4);
pVerticalDynamics->StepExplicit(2, 1, timeSub4, dtSub4);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Store the evaluation Kh4 to index 10
pGrid->LinearCombineData(m_dKh4Combo, 10, DataType_State);
// Compute u4 from uf4 and store it to index 2 (over u3)
dtSub4 = m_dImpCf[4][4] * dDeltaT;
//pGrid->CopyData(1, 2, DataType_State);
// Start with the previous data sum here because of the explicit zero
pGrid->LinearCombineData(m_du4fCombo, 2, DataType_State);
pVerticalDynamics->StepImplicit(2, 2, timeSub4, dtSub4);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// Store the evaluation K4 to index 11
pGrid->LinearCombineData(m_dK4Combo, 11, DataType_State);
//std::cout << "Substage 4 done ... \n";
// SUBSTAGE 5
// Compute uf5 from u4 and store it to index 2
Time timeSub5 = time;
double dtSub5 = m_dExpCf[5][4] * dDeltaT;
pGrid->LinearCombineData(m_du5fCombo, 1, DataType_State);
pHorizontalDynamics->StepExplicit(2, 1, timeSub5, dtSub5);
pVerticalDynamics->StepExplicit(2, 1, timeSub5, dtSub5);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Store the evaluation Kh5 to index 12
pGrid->LinearCombineData(m_dKh5Combo, 12, DataType_State);
// Compute u5 from uf5 and store it to index 2 (over u4)
dtSub5 = m_dImpCf[5][5] * dDeltaT;
pGrid->CopyData(1, 2, DataType_State);
pVerticalDynamics->StepImplicit(1, 2, timeSub5, dtSub5);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// Store the evaluation K5 to index 13
pGrid->LinearCombineData(m_dK5Combo, 13, DataType_State);
//std::cout << "Substage 5 done ... \n";
// SUBSTAGE 6
// Compute uf6 from u5 and store it to index 2
Time timeSub6 = time;
double dtSub6 = m_dExpCf[6][5] * dDeltaT;
pGrid->LinearCombineData(m_du6fCombo, 1, DataType_State);
pHorizontalDynamics->StepExplicit(2, 1, timeSub6, dtSub6);
pVerticalDynamics->StepExplicit(2, 1, timeSub6, dtSub6);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
// Compute u5 from uf5 and store it to index 2 (over u4)
dtSub5 = m_dImpCf[6][6] * dDeltaT;
pGrid->CopyData(1, 2, DataType_State);
pVerticalDynamics->StepImplicit(1, 2, timeSub6, dtSub6);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
// Apply hyperdiffusion at the end of the explicit substep (ask Paul)
pGrid->CopyData(2, 1, DataType_State);
pHorizontalDynamics->StepAfterSubCycle(2, 1, 3, time, dDeltaT);
pGrid->CopyData(1, 0, DataType_State);
//*/
}
void TimestepSchemeStrang::Step(
bool fFirstStep,
bool fLastStep,
const Time & time,
double dDeltaT
) {
// Get a copy of the grid
Grid * pGrid = m_model.GetGrid();
// Get a copy of the HorizontalDynamics
HorizontalDynamics * pHorizontalDynamics =
m_model.GetHorizontalDynamics();
// Get a copy of the VerticalDynamics
VerticalDynamics * pVerticalDynamics =
m_model.GetVerticalDynamics();
// Half a time step
double dHalfDeltaT = 0.5 * dDeltaT;
// Vertical timestep
if (fFirstStep) {
pVerticalDynamics->StepImplicit(0, 0, time, dHalfDeltaT);
} else {
pGrid->LinearCombineData(m_dCarryoverCombination, 0, DataType_State);
}
// Forward Euler
if (m_eExplicitDiscretization == ForwardEuler) {
pGrid->CopyData(0, 4, DataType_State);
pHorizontalDynamics->StepExplicit(0, 4, time, dDeltaT);
pVerticalDynamics->StepExplicit(0, 4, time, dDeltaT);
pGrid->PostProcessSubstage(4, DataType_State);
pGrid->PostProcessSubstage(4, DataType_Tracers);
// Explicit fourth-order Runge-Kutta
} else if (m_eExplicitDiscretization == RungeKutta4) {
pGrid->CopyData(0, 1, DataType_State);
pHorizontalDynamics->StepExplicit(0, 1, time, dHalfDeltaT);
pVerticalDynamics->StepExplicit(0, 1, time, dHalfDeltaT);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
pGrid->CopyData(0, 2, DataType_State);
pHorizontalDynamics->StepExplicit(1, 2, time, dHalfDeltaT);
pVerticalDynamics->StepExplicit(1, 2, time, dHalfDeltaT);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
pGrid->CopyData(0, 3, DataType_State);
pHorizontalDynamics->StepExplicit(2, 3, time, dDeltaT);
pVerticalDynamics->StepExplicit(2, 3, time, dDeltaT);
pGrid->PostProcessSubstage(3, DataType_State);
pGrid->PostProcessSubstage(3, DataType_Tracers);
pGrid->LinearCombineData(m_dRK4Combination, 4, DataType_State);
pHorizontalDynamics->StepExplicit(3, 4, time, dDeltaT / 6.0);
pVerticalDynamics->StepExplicit(3, 4, time, dDeltaT / 6.0);
pGrid->PostProcessSubstage(4, DataType_State);
pGrid->PostProcessSubstage(4, DataType_Tracers);
// Explicit strong stability preserving third-order Runge-Kutta
} else if (m_eExplicitDiscretization == RungeKuttaSSP3) {
pGrid->CopyData(0, 1, DataType_State);
pHorizontalDynamics->StepExplicit(0, 1, time, dDeltaT);
pVerticalDynamics->StepExplicit(0, 1, time, dDeltaT);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
pGrid->LinearCombineData(m_dSSPRK3CombinationA, 2, DataType_State);
pHorizontalDynamics->StepExplicit(1, 2, time, 0.25 * dDeltaT);
pVerticalDynamics->StepExplicit(1, 2, time, 0.25 * dDeltaT);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
pGrid->LinearCombineData(m_dSSPRK3CombinationB, 4, DataType_State);
pHorizontalDynamics->StepExplicit(2, 4, time, (2.0/3.0) * dDeltaT);
pVerticalDynamics->StepExplicit(2, 4, time, (2.0/3.0) * dDeltaT);
pGrid->PostProcessSubstage(4, DataType_State);
pGrid->PostProcessSubstage(4, DataType_Tracers);
// Explicit Kinnmark, Gray and Ullrich third-order five-stage Runge-Kutta
} else if (m_eExplicitDiscretization == KinnmarkGrayUllrich35) {
pGrid->CopyData(0, 1, DataType_State);
pHorizontalDynamics->StepExplicit(0, 1, time, dDeltaT / 5.0);
pVerticalDynamics->StepExplicit(0, 1, time, dDeltaT / 5.0);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
pGrid->CopyData(0, 2, DataType_State);
pHorizontalDynamics->StepExplicit(1, 2, time, dDeltaT / 5.0);
pVerticalDynamics->StepExplicit(1, 2, time, dDeltaT / 5.0);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
pGrid->CopyData(0, 3, DataType_State);
pHorizontalDynamics->StepExplicit(2, 3, time, dDeltaT / 3.0);
pVerticalDynamics->StepExplicit(2, 3, time, dDeltaT / 3.0);
pGrid->PostProcessSubstage(3, DataType_State);
pGrid->PostProcessSubstage(3, DataType_Tracers);
pGrid->CopyData(0, 2, DataType_State);
pHorizontalDynamics->StepExplicit(3, 2, time, 2.0 * dDeltaT / 3.0);
pVerticalDynamics->StepExplicit(3, 2, time, 2.0 * dDeltaT / 3.0);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
pGrid->LinearCombineData(
m_dKinnmarkGrayUllrichCombination, 4, DataType_State);
pHorizontalDynamics->StepExplicit(2, 4, time, 3.0 * dDeltaT / 4.0);
pVerticalDynamics->StepExplicit(2, 4, time, 3.0 * dDeltaT / 4.0);
pGrid->PostProcessSubstage(4, DataType_State);
pGrid->PostProcessSubstage(4, DataType_Tracers);
// Explicit strong stability preserving five-stage third-order Runge-Kutta
} else if (m_eExplicitDiscretization == RungeKuttaSSPRK53) {
const double dStepOne = 0.377268915331368;
pGrid->CopyData(0, 1, DataType_State);
pHorizontalDynamics->StepExplicit(0, 1, time, dStepOne * dDeltaT);
pVerticalDynamics->StepExplicit(0, 1, time, dStepOne * dDeltaT);
pGrid->PostProcessSubstage(1, DataType_State);
pGrid->PostProcessSubstage(1, DataType_Tracers);
pGrid->CopyData(1, 2, DataType_State);
pHorizontalDynamics->StepExplicit(1, 2, time, dStepOne * dDeltaT);
pVerticalDynamics->StepExplicit(1, 2, time, dStepOne * dDeltaT);
pGrid->PostProcessSubstage(2, DataType_State);
pGrid->PostProcessSubstage(2, DataType_Tracers);
const double dStepThree = 0.242995220537396;
pGrid->LinearCombineData(m_dSSPRK53CombinationA, 3, DataType_State);
pHorizontalDynamics->StepExplicit(2, 3, time, dStepThree * dDeltaT);
pVerticalDynamics->StepExplicit(2, 3, time, dStepThree * dDeltaT);
pGrid->PostProcessSubstage(3, DataType_State);
pGrid->PostProcessSubstage(3, DataType_Tracers);
const double dStepFour = 0.238458932846290;
pGrid->LinearCombineData(m_dSSPRK53CombinationB, 0, DataType_State);
pHorizontalDynamics->StepExplicit(3, 0, time, dStepFour * dDeltaT);
pVerticalDynamics->StepExplicit(3, 0, time, dStepFour * dDeltaT);
pGrid->PostProcessSubstage(0, DataType_State);
pGrid->PostProcessSubstage(0, DataType_Tracers);
const double dStepFive = 0.287632146308408;
pGrid->LinearCombineData(m_dSSPRK53CombinationC, 4, DataType_State);
pHorizontalDynamics->StepExplicit(0, 4, time, dStepFive * dDeltaT);
pVerticalDynamics->StepExplicit(0, 4, time, dStepFive * dDeltaT);
pGrid->PostProcessSubstage(4, DataType_State);
pGrid->PostProcessSubstage(4, DataType_Tracers);
// Invalid explicit discretization
} else {
_EXCEPTIONT("Invalid explicit discretization");
}
// Apply hyperdiffusion
pGrid->CopyData(4, 1, DataType_State);
pHorizontalDynamics->StepAfterSubCycle(4, 1, 2, time, dDeltaT);
// Vertical timestep
double dOffCenterDeltaT = 0.5 * (1.0 + m_dOffCentering) * dDeltaT;
pGrid->CopyData(1, 0, DataType_State);
pVerticalDynamics->StepImplicit(0, 0, time, dOffCenterDeltaT);
pGrid->LinearCombineData(m_dOffCenteringCombination, 0, DataType_State);
if (!fLastStep) {
pGrid->LinearCombineData(m_dCarryoverFinal, 1, DataType_State);
}
//pGrid->CopyData(0, 1, DataType_State);
//pVerticalDynamics->StepExplicit(0, 1, time, dDeltaT);
//pVerticalDynamics->StepImplicit(0, 0, time, dDeltaT);
/*
if (0) {
//if (fLastStep) {
DataVector<double> dDifference;
dDifference.Initialize(2);
dDifference[0] = -1.0;
dDifference[1] = 1.0;
pGrid->LinearCombineData(dDifference, 0, DataType_State);
} else {
pGrid->CopyData(4, 0, DataType_State);
}
*/
}
