Fluid model

ViscoResistiveMHD_with_p

Full (non-linear) visco-resistive MHD equations, with the pressure variable, discretized with a variational method.

Overview

This is the pressure-based full nonlinear dissipative MHD model. It is

the natural counterpart to the entropy- and q-based full MHD variants when pressure is preferred as primitive thermodynamic variable.

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) + \frac{1}{γ - 1} \nabla p + B \times \nabla \times B - \nabla \cdot ((μ + μ_{a} (x)) \nabla u) = 0

Pressure:

\partial_{t} p + u \cdot \nabla p + γ p \nabla \cdot u = \frac{1}{γ - 1} ((μ + μ_{a} (x)) ∣\nabla u ∣^{2} + (η + η_{a} (x)) ∣\nabla \times B ∣^{2})

Induction:

\partial_{t} B + \nabla \times (B \times u) + \nabla \times (η + η_{a} (x)) \nabla \times B = 0

Here $μ_{a} (x)$ and $η_{a} (x)$ are artificial viscosity and resistivity coefficients.

The characteristic flow speed is the Alfvén speed,

u^= v^_{A} .

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_pb_evolve.VariationalPBEvolve
struphy.propagators.variational_viscosity.VariationalViscosity (if with_viscosity is True)
struphy.propagators.variational_resistivity.VariationalResistivity (if with_resistivity is True)

Create and initialize the pressure-based visco-resistive MHD model:

from struphy.models import ViscoResistiveMHD_with_p

model = ViscoResistiveMHD_with_p()
model.mhd.pressure

model.em_fields.b_field