scalar cnoidalFirst::ddxPd
(
const point & x,
const scalar & time,
const vector & unitVector
) const
{
scalar Z(returnZ(x));
scalar arg(argument(x,time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar ddxPd(0);
ddxPd = rhoWater_ * Foam::mag(g_)
* (
eta_x(snn, cnn, dnn) + 1.0 / 2.0 * Foam::pow(h_, 2.0) * (1 - Foam::pow((Z + h_) / h_, 2.0)) * eta_xxx(snn, cnn, dnn)
);
ddxPd *= factor(time);
// Info << "ddxPd still isn't implemented. Need to think about the gradient on arbitrary directed mesh with arbitrary wave number vector! and arbitrary g-direction!!!" << endl;
return ddxPd;
}
vector cnoidalFirst::U
(
const point & x,
const scalar & time
) const
{
scalar Z(returnZ(x));
scalar arg(argument(x, time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar etaVal = eta(x,time);
scalar Uhorz = celerity_
* (
etaVal / h_
- Foam::pow(etaVal / h_, 2.0)
+ 1.0 / 2.0 *
(
1.0 / 3.0
- Foam::pow((Z + h_) / h_, 2.0)
)
* h_ * eta_xx(snn, cnn, dnn)
);
Uhorz *= factor(time);
scalar Uvert = - celerity_ * (Z + h_)
* (
eta_x(snn, cnn, dnn) / h_ * (1 - 2.0 * etaVal / h_)
+ 1.0 / 6.0 * h_ * eta_xxx(snn, cnn, dnn)
* (1 - Foam::pow((Z + h_) / h_, 2.0))
);
Uvert *= factor(time);
return Uhorz * propagationDirection_ - Uvert * direction_; // Note "-" because of "g" working in the opposite direction
}
void
PetscCompGridVTO::createOpStencil(IntVect a_iv, int a_ilev,const DataIndex &a_di, StencilTensor &a_sten)
{
CH_TIME("PetscCompGridVTO::createOpStencil");
Real dx=m_dxs[a_ilev][0],idx2=1./(dx*dx);
Real eta_x0,eta_x1,lam_x0,lam_x1,eta_y0,eta_y1,lam_y0,lam_y1;
IntVect ivwst=IntVect::Zero,ivest=IntVect::Zero,ivsth=IntVect::Zero,ivnth=IntVect::Zero;
//IntVect ivSW(-1,-1),ivSE(1,-1),ivNE(1,1),ivNW(-1,1);
IntVect ivSW(IntVect::Unit),ivSE(IntVect::Unit),ivNE(IntVect::Unit),ivNW(IntVect::Unit);
ivSW[1] = ivSW[0] = -1; // >= 2D
ivSE[1] = -1; // >= 2D
ivNW[0] = -1;
ivwst[0] = -1; ivest[0] = 1; ivsth[1] = -1; ivnth[1] = 1;
{ // get stencil coeficients
Real beta_hinv2=m_beta*idx2;
const FluxBox &etaFab = (*m_eta[a_ilev])[a_di];
const FArrayBox &eta_x = etaFab[0];
const FArrayBox &eta_y = etaFab[1];
const FluxBox &lamFab = (*m_lamb[a_ilev])[a_di];
const FArrayBox &lam_x = lamFab[0];
const FArrayBox &lam_y = lamFab[1];
eta_x0 = beta_hinv2*eta_x(a_iv,0); eta_y0 = beta_hinv2*eta_y(a_iv,0);
eta_x1 = beta_hinv2*eta_x(ivest+a_iv,0); eta_y1 = beta_hinv2*eta_y(ivnth+a_iv,0);
lam_x0 = beta_hinv2*lam_x(a_iv,0); lam_y0 = beta_hinv2*lam_y(a_iv,0);
lam_x1 = beta_hinv2*lam_x(ivest+a_iv,0); lam_y1 = beta_hinv2*lam_y(ivnth+a_iv,0);
}
// loop over two equations, should probably just hard wire this
for (int kk=0,vv=1;kk<2;kk++,vv--)
{
Real vd;
// add one eta everywhere -- same for u and v
vd = eta_x0;
{
StencilTensorValue &v1 = a_sten[IndexML(ivwst+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = eta_x1;
{
StencilTensorValue &v1 = a_sten[IndexML(ivest+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = eta_y0;
{
StencilTensorValue &v1 = a_sten[IndexML(ivsth+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = eta_y1;
{
StencilTensorValue &v1 = a_sten[IndexML(ivnth+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = -(eta_x0 + eta_y0 + eta_x1 + eta_y1);
{
StencilTensorValue &v1 = a_sten[IndexML(a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
// add extra eta and the lambda for each direction
if (kk==0)
{
vd = eta_x0 + lam_x0;
{
StencilTensorValue &v1 = a_sten[IndexML(ivwst+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = eta_x1 + lam_x1;
{
StencilTensorValue &v1 = a_sten[IndexML(ivest+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = -(eta_x0 + eta_x1 + lam_x0 + lam_x1);
{
StencilTensorValue &v1 = a_sten[IndexML(a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
}
else {
vd = eta_y0 + lam_y0;
{
StencilTensorValue &v1 = a_sten[IndexML(ivsth+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = eta_y1 + lam_y1;
{
StencilTensorValue &v1 = a_sten[IndexML(ivnth+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
vd = -(eta_y0 + eta_y1 + lam_y0 + lam_y1);
{
StencilTensorValue &v1 = a_sten[IndexML(a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
}
// u -- v coupling terms -- 8 point stencil
// S
if (kk==0) vd = 0.25*(-lam_x1 + lam_x0);
else vd = 0.25*(-eta_x1 + eta_x0);
{
StencilTensorValue &v1 = a_sten[IndexML(ivsth+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// S.W.
if (kk==0) vd = 0.25*(eta_y0 + lam_x0);
else vd = 0.25*(eta_x0 + lam_y0);
{
StencilTensorValue &v1 = a_sten[IndexML(ivSW+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// S.E.
if (kk==0) vd = 0.25*(-lam_x1 - eta_y0);
else vd = 0.25*(-lam_y0 - eta_x1);
{
StencilTensorValue &v1 = a_sten[IndexML(ivSE+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// W
if (kk==0) vd = 0.25*(-eta_y1 + eta_y0);
else vd = 0.25*(-lam_y1 + lam_y0);
{
StencilTensorValue &v1 = a_sten[IndexML(ivwst+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// E
if (kk==0) vd = 0.25*(eta_y1 - eta_y0);
else vd = 0.25*(lam_y1 - lam_y0);
{
StencilTensorValue &v1 = a_sten[IndexML(ivest+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// N.W.
if (kk==0) vd = 0.25*(-lam_x0 - eta_y1);
else vd = 0.25*(-lam_y1 - eta_x0);
{
StencilTensorValue &v1 = a_sten[IndexML(ivNW+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// N
if (kk==0) vd = 0.25*(lam_x1 - lam_x0);
else vd = 0.25*(eta_x1 - eta_x0);
{
StencilTensorValue &v1 = a_sten[IndexML(ivnth+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// N.E.
if (kk==0) vd = 0.25*(eta_y1 + lam_x1);
else vd = 0.25*(eta_x1 + lam_y1);
{
StencilTensorValue &v1 = a_sten[IndexML(ivNE+a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,vv,vd);
}
// diagonal alpha term
vd = m_alpha * (!(m_a[a_ilev]) ? 1. : (*m_a[a_ilev])[a_di](a_iv,0));
{
StencilTensorValue &v1 = a_sten[IndexML(a_iv,a_ilev)]; v1.define(CH_SPACEDIM);
v1.addValue(kk,kk,vd);
}
} // kk=1:2 loop
if (0)
{
Real summ=0.;
StencilTensor::const_iterator end = a_sten.end();
for ( StencilTensor::const_iterator it = a_sten.begin(); it != end; ++it) {
for (int i=0; i<CH_SPACEDIM; ++i)
{
for (int j=0; j<CH_SPACEDIM; ++j)
{
summ += it->second.value(i,j);
}
}
}
if (abs(summ>1.e-10))
{
for (StencilTensor::const_iterator it = a_sten.begin(); it != end; ++it) {
pout() << it->first << " ERROR: \n";
for (int i=0; i<CH_SPACEDIM; ++i)
{
pout() << "\t\t";
for (int j=0; j<CH_SPACEDIM; ++j)
{
pout() << it->second.value(i,j) << ", ";
}
pout() << endl;
}
}
pout() << "\t ERROR summ: " << summ << endl;
}
}
}
