def flux(self):
from grudge.flux import make_normal, FluxVectorPlaceholder
v = FluxVectorPlaceholder(self.arg_count)
normal = make_normal(self.dimensions)
flux = 0
idx = 0
for i, i_enabled in enumerate(self.subset):
if i_enabled and i < self.dimensions:
flux += (v.int - v.avg)[idx] * normal[i]
idx += 1
return flux
def get_advection_flux(self, velocity):
from grudge.flux import make_normal, FluxScalarPlaceholder
from pymbolic.primitives import IfPositive
u = FluxScalarPlaceholder(0)
normal = make_normal(self.method.dimensions)
if self.flux_type == "central":
return u.avg * np.dot(normal, velocity)
elif self.flux_type == "lf":
return u.avg*np.dot(normal, velocity) \
+ 0.5*la.norm(v)*(u.int - u.ext)
elif self.flux_type == "upwind":
return (np.dot(normal, velocity) * IfPositive(
np.dot(normal, velocity),
u.int, # outflow
u.ext, # inflow
))
else:
raise ValueError("invalid flux type")
def flux(self):
from grudge.flux import make_normal, FluxScalarPlaceholder
u = FluxScalarPlaceholder()
normal = make_normal(self.dimensions)
return u.int * normal - u.avg * normal
def normal_times_flux(self, flux):
from grudge.flux import make_normal
return self.vec_times(make_normal(self.dimensions), flux)