Fluid model

ViscoResistiveLinearMHD_with_q

Linear visco-resistive MHD equations, with the q variable (square root of the pressure), discretized with a variational method.

Overview

This variant of the linear dissipative MHD model uses the square root

of the pressure as primary thermodynamic variable, which is convenient for the corresponding variational discretization.

This model is appropriate for:

Continuity:

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

Momentum:

\partial_{t} (ρ_{0} u ~) + \frac{2 q _{0}}{γ - 1} \nabla q ~ + \frac{2 q ~}{γ - 1} \nabla q_{0} + B_{0} \times \nabla \times B ~ + B ~ \times \nabla \times B_{0} - \nabla \cdot ((μ + μ_{a} (x)) \nabla u ~) = 0

Energy-like variable:

\partial_{t} q ~ + \nabla q_{0} \cdot u ~ + (\frac{γ}{2} - 1) q_{0} \nabla \cdot u ~ = 0

Induction:

\partial_{t} B ~ + \nabla \times (B_{0} \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 flow normalization is Alfvénic:

u^= v^_{A} .

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

struphy.propagators.variational_density_evolve.VariationalDensityEvolve
struphy.propagators.variational_qb_evolve.VariationalQBEvolve
struphy.propagators.variational_viscosity.VariationalViscosity (if with_viscosity is True)
struphy.propagators.variational_resistivity.VariationalResistivity (if with_resistivity is True)

Create and initialize the linear visco-resistive q-MHD model:

from struphy.models import ViscoResistiveLinearMHD_with_q

model = ViscoResistiveLinearMHD_with_q()
model.mhd.sqrt_p

model.em_fields.b_field