A novel structure preserving semi‐implicit finite volume method for viscous and resistive magnetohydrodynamics

In this work we introduce a novel semi-implicit structure-preserving finite-volume/finite-difference scheme for the viscous and resistive equations of magnetohydrodynamics (MHD) based on an appropriate 3-split governing PDE system, which is decomposed into first convective subsystem, second subsystem involving coupling velocity field with magnetic third pressure-velocity coupling. The nonlinear terms are discretized explicitly, while remaining two subsystems accounting Alfven waves magneto-acoustic treated implicitly. final algorithm at least formally constrained only by mild CFL stability condition depending pure hydrodynamic convection. To preserve divergence-free constraint exactly discrete level, proper set overlapping dual meshes employed. resulting linear algebraic systems shown to be symmetric therefore can solved means efficient standard matrix-free conjugate gradient algorithm. One peculiarities presented that defined edges main grid, electric faces. regarded as shock-capturing, conservative structure preserving MHD equations. Several numerical tests show features our solver: linear-stability in sense Lyapunov verified prescribed constant equilibrium solution; 2nd-order convergence numerically estimated; shock-capturing capabilities proven against stringent shock-problems; accuracy robustness nontrivial 2- 3-dimensional problems.