inline double
compute_linear_extrap(
D& patch_data,
const I& i,
const I& i_intr,
const IntVector<NDIM>& i_shft,
const int depth)
{
double ret_val = patch_data(i_intr,depth);
for (unsigned int d = 0; d < NDIM; ++d)
{
if (i_shft(d) != 0)
{
const I& i_intr0 = i_intr;
I i_intr1 = i_intr;
i_intr1(d) += i_shft(d);
const double& f0 = patch_data(i_intr0,depth);
const double& f1 = patch_data(i_intr1,depth);
const double du = f0-f1;
const double delta = std::abs(i(d)-i_intr(d));
ret_val += du*delta;
}
}
return ret_val;
}// compute_linear_extrap
inline double
compute_quadratic_extrap(D& patch_data,
const I& i,
const I& i_intr,
const IntVector<NDIM>& i_shft,
const int depth,
const int codim)
{
if (codim == 1)
{
for (unsigned int d = 0; d < NDIM; ++d)
{
if (i_shft(d) != 0)
{
const I& i_intr0 = i_intr;
I i_intr1 = i_intr;
i_intr1(d) += i_shft(d);
I i_intr2 = i_intr1;
i_intr2(d) += i_shft(d);
const double& f0 = patch_data(i_intr0, depth);
const double& f1 = patch_data(i_intr1, depth);
const double& f2 = patch_data(i_intr2, depth);
const double x = std::abs(i(d) - i_intr(d));
return (1.0 / 2.0 * f2 - f1 + 1.0 / 2.0 * f0) * x * x +
(-1.0 / 2.0 * f2 + 2.0 * f1 - 3.0 / 2.0 * f0) * x + f0;
}
}
}
else
{
return compute_linear_extrap(patch_data, i, i_intr, i_shft, depth);
}
return 0.0; // this statement should not be reached
} // compute_quadratic_extrap
inline double
compute_quadratic_extrap(
D& patch_data,
const I& i,
const I& i_intr,
const IntVector<NDIM>& i_shft,
const int depth,
const int codim)
{
if (codim == 1)
{
for (unsigned int d = 0; d < NDIM; ++d)
{
if (i_shft(d) != 0)
{
#if 1
const I& i_intr0 = i_intr;
I i_intr1 = i_intr;
i_intr1(d) += i_shft(d);
I i_intr2 = i_intr1;
i_intr2(d) += i_shft(d);
const double& f0 = patch_data(i_intr0,depth);
const double& f1 = patch_data(i_intr1,depth);
const double& f2 = patch_data(i_intr2,depth);
const double x = std::abs(i(d)-i_intr(d));
return (1.0/2.0*f2-f1+1.0/2.0*f0)*x*x+(-1.0/2.0*f2+2.0*f1-3.0/2.0*f0)*x+f0;
#endif
#if 0
// NOTE: The following only works in general for the case that
// the ghost cell width is >= 3.
const I& i_intr0 = i_intr;
I i_intr2 = i_intr;
i_intr2(d) += 2*i_shft(d);
I i_intr3 = i_intr2;
i_intr3(d) += i_shft(d);
const double& f0 = patch_data(i_intr0,depth);
const double& f2 = patch_data(i_intr2,depth);
const double& f3 = patch_data(i_intr3,depth);
const double x = std::abs(i(d)-i_intr(d));
return (1.0/3.0*f3-1.0/2.0*f2+1.0/6.0*f0)*x*x+(-2.0/3.0*f3+3.0/2.0*f2-5.0/6.0*f0)*x+f0;
#endif
}
}
}
else
{
return compute_linear_extrap(patch_data, i, i_intr, i_shft, depth);
}
return 0.0; // this statement should not be reached
}// compute_quadratic_extrap
void
AdvDiffPhysicalBoundaryUtilities::setPhysicalBoundaryConditions(
Pointer<CellData<NDIM,double> > Q_data,
Pointer<FaceData<NDIM,double> > u_ADV_data,
Pointer<Patch<NDIM> > patch,
const std::vector<RobinBcCoefStrategy<NDIM>*>& bc_coefs,
const double fill_time,
const bool inflow_boundaries_only,
const bool homogeneous_bc)
{
Pointer<CartesianPatchGeometry<NDIM> > pgeom = patch->getPatchGeometry();
if (!pgeom->getTouchesRegularBoundary()) return;
const Array<BoundaryBox<NDIM> > physical_codim1_boxes = PhysicalBoundaryUtilities::getPhysicalBoundaryCodim1Boxes(*patch);
if (physical_codim1_boxes.size() == 0) return;
// Loop over the boundary fill boxes and set boundary conditions.
const Box<NDIM>& patch_box = patch->getBox();
const double* const dx = pgeom->getDx();
// Setup any extended Robin BC coef objects.
for (int depth = 0; depth < Q_data->getDepth(); ++depth)
{
ExtendedRobinBcCoefStrategy* extended_bc_coef = dynamic_cast<ExtendedRobinBcCoefStrategy*>(bc_coefs[depth]);
if (extended_bc_coef)
{
extended_bc_coef->clearTargetPatchDataIndex();
extended_bc_coef->setHomogeneousBc(homogeneous_bc);
}
}
// Set the boundary conditions.
const IntVector<NDIM>& gcw = Q_data->getGhostCellWidth();
for (int n = 0; n < physical_codim1_boxes.size(); ++n)
{
const BoundaryBox<NDIM>& bdry_box = physical_codim1_boxes[n];
const unsigned int location_index = bdry_box.getLocationIndex();
const unsigned int bdry_normal_axis = location_index/2;
const bool is_lower = location_index%2 == 0;
static const IntVector<NDIM> gcw_to_fill = 1;
const Box<NDIM> bc_fill_box = pgeom->getBoundaryFillBox(bdry_box, patch_box, gcw_to_fill);
const BoundaryBox<NDIM> trimmed_bdry_box(bdry_box.getBox() * bc_fill_box, bdry_box.getBoundaryType(), bdry_box.getLocationIndex());
Box<NDIM> bc_coef_box = PhysicalBoundaryUtilities::makeSideBoundaryCodim1Box(trimmed_bdry_box);
for (unsigned int d = 0; d < NDIM; ++d)
{
if (d != bdry_normal_axis)
{
bc_coef_box.lower(d) = std::max(bc_coef_box.lower(d), patch_box.lower(d));
bc_coef_box.upper(d) = std::min(bc_coef_box.upper(d), patch_box.upper(d));
}
}
Pointer<ArrayData<NDIM,double> > acoef_data = new ArrayData<NDIM,double>(bc_coef_box, 1);
Pointer<ArrayData<NDIM,double> > bcoef_data = new ArrayData<NDIM,double>(bc_coef_box, 1);
Pointer<ArrayData<NDIM,double> > gcoef_data = new ArrayData<NDIM,double>(bc_coef_box, 1);
for (int depth = 0; depth < Q_data->getDepth(); ++depth)
{
bc_coefs[depth]->setBcCoefs(acoef_data, bcoef_data, gcoef_data, NULL, *patch, trimmed_bdry_box, fill_time);
ExtendedRobinBcCoefStrategy* extended_bc_coef = dynamic_cast<ExtendedRobinBcCoefStrategy*>(bc_coefs[depth]);
if (homogeneous_bc && !extended_bc_coef) gcoef_data->fillAll(0.0);
for (Box<NDIM>::Iterator bc(bc_coef_box); bc; bc++)
{
const Index<NDIM>& i = bc();
const FaceIndex<NDIM> i_f(i, bdry_normal_axis, FaceIndex<NDIM>::Lower);
bool is_inflow_bdry = (is_lower && (*u_ADV_data)(i_f) > 0.0) || (!is_lower && (*u_ADV_data)(i_f) < 0.0);
if (!inflow_boundaries_only || is_inflow_bdry)
{
const double& a = (*acoef_data)(i,0);
const double& b = (*bcoef_data)(i,0);
const double& g = (*gcoef_data)(i,0);
const double& h = dx[bdry_normal_axis];
int sgn;
Index<NDIM> i_intr(i);
if (is_lower)
{
sgn = -1;
}
else
{
sgn = +1;
i_intr(bdry_normal_axis) -= 1;
}
Index<NDIM> i_true(i_intr), i_ghost(i_intr);
for (int k = 1; k <= gcw(bdry_normal_axis); ++k)
{
i_ghost(bdry_normal_axis) = i_intr(bdry_normal_axis) + sgn*k;
i_true (bdry_normal_axis) = i_intr(bdry_normal_axis) - sgn*(k-1);
const double Q_i = (*Q_data)(i_true,depth);
(*Q_data)(i_ghost,depth) = -(-4.0*g*h*k-2.0*g*h+2.0*a*Q_i*h*k+a*Q_i*h-2.0*b*Q_i)/(2.0*a*h*k+a*h+2.0*b);
}
}
}
}
}
return;
}// setPhysicalBoundaryConditions
