Fluid model

ViscoResistiveDeltafMHD_with_q

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

Overview

This model is the delta f dissipative MHD formulation in the

q-variable representation. It is aimed at perturbative nonlinear MHD studies where the q-formulation is preferred numerically.

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

Induction:

\partial_{t} B ~ + \nabla \times ((B_{0} + 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 model uses Alfvén-speed normalization:

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_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 visco-resistive delta f q-MHD model:

from struphy.models import ViscoResistiveDeltafMHD_with_q

model = ViscoResistiveDeltafMHD_with_q()
model.mhd.sqrt_p

model.em_fields.b_field