std::vector<RealGradient>
CNSFVMinmaxSlopeLimiting::limitElementSlope() const
{
const Elem * elem = _current_elem;
/// current element id
dof_id_type _elementID = elem->id();
/// current element centroid coordinte
Point ecent = elem->centroid();
/// number of sides surrounding an element
unsigned int nside = elem->n_sides();
/// number of conserved variables
unsigned int nvars = 5;
/// vector for the centroid of the sides surrounding an element
std::vector<Point> scent(nside, Point(0., 0., 0.));
/// vector for the limited gradients of the conserved variables
std::vector<RealGradient> ugrad(nvars, RealGradient(0., 0., 0.));
/// a flag to indicate the boundary side of the current cell
bool bflag = false;
/// initialize local minimum variable values
std::vector<Real> umin(nvars, 0.);
/// initialize local maximum variable values
std::vector<Real> umax(nvars, 0.);
/// initialize local cache for element variable values
std::vector<Real> uelem(nvars, 0.);
/// initialize local cache for reconstructed element gradients
std::vector<RealGradient> rugrad(nvars, RealGradient(0., 0., 0.));
/// initialize local cache for element slope limitor values
std::vector<std::vector<Real>> limit(nside + 1, std::vector<Real>(nvars, 1.));
Real dij = 0.;
uelem = _rslope.getElementAverageValue(_elementID);
for (unsigned int iv = 0; iv < nvars; iv++)
{
umin[iv] = uelem[iv];
umax[iv] = uelem[iv];
}
/// loop over the sides to find the min and max cell-average values
for (unsigned int is = 0; is < nside; is++)
{
const Elem * neighbor = elem->neighbor_ptr(is);
if (neighbor != nullptr && this->hasBlocks(neighbor->subdomain_id()))
{
dof_id_type _neighborID = neighbor->id();
uelem = _rslope.getElementAverageValue(_neighborID);
scent[is] = _rslope.getSideCentroid(_elementID, _neighborID);
}
else
{
uelem = _rslope.getBoundaryAverageValue(_elementID, is);
scent[is] = _rslope.getBoundarySideCentroid(_elementID, is);
}
for (unsigned int iv = 0; iv < nvars; iv++)
{
if (uelem[iv] < umin[iv])
umin[iv] = uelem[iv];
if (uelem[iv] > umax[iv])
umax[iv] = uelem[iv];
}
}
/// loop over the sides to compute the limiter values
rugrad = _rslope.getElementSlope(_elementID);
uelem = _rslope.getElementAverageValue(_elementID);
for (unsigned int is = 0; is < nside; is++)
{
for (unsigned int iv = 0; iv < nvars; iv++)
{
dij = (scent[is] - ecent) * rugrad[iv];
if (dij > 0.)
limit[is + 1][iv] = std::min(1., (umax[iv] - uelem[iv]) / dij);
else if (dij < 0.)
limit[is + 1][iv] = std::min(1., (umin[iv] - uelem[iv]) / dij);
}
}
/// loop over the sides to get the final limiter of this cell
for (unsigned int is = 0; is < nside; is++)
{
for (unsigned int iv = 0; iv < nvars; iv++)
{
if (limit[0][iv] > limit[is + 1][iv])
limit[0][iv] = limit[is + 1][iv];
}
}
/// get the limited slope of this cell
if (!_include_bc && bflag)
{
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] = RealGradient(0., 0., 0.);
}
else
{
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] = rugrad[iv] * limit[0][iv];
}
return ugrad;
}
std::vector<RealGradient>
CNSFVWENOSlopeLimiting::limitElementSlope() const
{
const Elem * elem = _current_elem;
/// current element id
dof_id_type _elementID = elem->id();
/// number of conserved variables
unsigned int nvars = 5;
/// number of sides surrounding an element
unsigned int nside = elem->n_sides();
/// vector for the limited gradients of the conserved variables
std::vector<RealGradient> ugrad(nvars, RealGradient(0., 0., 0.));
/// initialize local cache for reconstructed element gradients
std::vector<RealGradient> rugrad(nvars, RealGradient(0., 0., 0.));
/// a small number to avoid dividing by zero
Real eps = 1e-7;
/// initialize oscillation indicator
std::vector<std::vector<Real>> osci(nside + 1, std::vector<Real>(nvars, 0.));
/// initialize weight coefficients
std::vector<std::vector<Real>> weig(nside + 1, std::vector<Real>(nvars, 0.));
/// initialize summed coefficients
std::vector<Real> summ(nvars, 0.);
/// compute oscillation indicators, nonlinear weights and their summ for each stencil
rugrad = _rslope.getElementSlope(_elementID);
for (unsigned int iv = 0; iv < nvars; iv++)
{
osci[0][iv] = std::sqrt(rugrad[iv] * rugrad[iv]);
weig[0][iv] = _lweig / std::pow(eps + osci[0][iv], _dpowe);
summ[iv] = weig[0][iv];
}
for (unsigned int is = 0; is < nside; is++)
{
unsigned int in = is + 1;
if (elem->neighbor(is) != NULL)
{
dof_id_type _neighborID = elem->neighbor(is)->id();
rugrad = _rslope.getElementSlope(_neighborID);
for (unsigned int iv = 0; iv < nvars; iv++)
{
osci[in][iv] = std::sqrt(rugrad[iv] * rugrad[iv]);
weig[in][iv] = 1. / std::pow(eps + osci[in][iv], _dpowe);
summ[iv] += weig[in][iv];
}
}
}
/// compute the normalized weight
for (unsigned int iv = 0; iv < nvars; iv++)
weig[0][iv] = weig[0][iv] / summ[iv];
for (unsigned int is = 0; is < nside; is++)
{
unsigned int in = is + 1;
if (elem->neighbor(is) != NULL)
for (unsigned int iv = 0; iv < nvars; iv++)
weig[in][iv] = weig[in][iv] / summ[iv];
}
/// compute the limited slope
rugrad = _rslope.getElementSlope(_elementID);
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] = weig[0][iv] * rugrad[iv];
for (unsigned int is = 0; is < nside; is++)
{
unsigned int in = is + 1;
if (elem->neighbor(is) != NULL)
{
dof_id_type _neighborID = elem->neighbor(is)->id();
rugrad = _rslope.getElementSlope(_neighborID);
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] += weig[in][iv] * rugrad[iv];
}
}
return ugrad;
}
