Fluid model

ViscousFluid

Full (non-linear) viscous Navier-Stokes equations discretized with a variational method.

Overview

ViscousFluid is the non-magnetic viscous member of the variational

fluid family. It is suited for compressible hydrodynamics with entropy transport and viscous heating but without magnetic effects.

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} - \nabla \cdot ((μ + μ_{a} (x)) \nabla u) = 0

Entropy:

\partial_{t} s + \nabla \cdot (s u) = \frac{1}{T} ((μ + μ_{a} (x)) ∣\nabla u ∣^{2})

where the internal energy per unit mass is $U (ρ) = ρ^{γ - 1} exp (s / ρ)$ . and $μ_{a} (x)$ is an artificial viscosity coefficient.

The model uses Alfvén-speed scaling for the velocity and entropy-based

thermodynamic units for the internal-energy closure.

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
struphy.propagators.variational_viscosity.VariationalViscosity (if with_viscosity is True)

Create and initialize a viscous-fluid model:

from struphy.models import ViscousFluid

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

model.fluid.entropy