Fluid model

VariationalCompressibleFluid

Fully compressible fluid equations discretized with a variational method.

Overview

VariationalCompressibleFluid is the entropy-based compressible fluid

model in the variational family. It is the natural non-magnetic counterpart to the full variational MHD models.

This model is appropriate for:

Continuity:

\partial_{t} ρ + \nabla \cdot (ρ u) = 0

Momentum:

\partial_{t} (ρ u) + \nabla \cdot (ρ u \otimes u) + ρ \nabla \frac{( ρ U ( ρ , s ))}{\partial ρ} + s \nabla \frac{( ρ U ( ρ , s ))}{\partial s} = 0

Entropy:

\partial_{t} s + \nabla \cdot (s u) = 0

where the internal energy per unit mass is $U (ρ) = ρ^{γ - 1} exp (s / ρ)$ .

The model uses Alfvén-speed scaling for the flow variables together

with separate units for internal energy and entropy:

u^= v^_{A}, U^= K, s^= ρ^C_{v} .

Time integration is performed by the following propagators (in sequence):

struphy.propagators.variational_density_evolve.VariationalDensityEvolve
struphy.propagators.variational_momentum_advection.VariationalMomentumAdvection
struphy.propagators.variational_entropy_evolve.VariationalEntropyEvolve

Create and initialize a variational compressible-fluid model:

from struphy.models import VariationalCompressibleFluid

model = VariationalCompressibleFluid()
model.fluid.density
model.fluid.velocity

model.fluid.entropy