High order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres

Wave propagation in idealized stellar atmospheres is modeled by the equations of ideal MHD, together with the gravity source term. The waves are modeled as small perturbations of isothermal steady states of the system. We consider a formulation of ideal MHD based on the Godunov–Powell form, with an embedded potential magnetic field appearing as a parameter. The equations are discretized by finite volume schemes based on approximate Riemann solvers of the HLL type and upwind discretizations of the Godunov–Powell source terms. Local hydrostatic reconstructions and suitable discretization of the gravity source term lead to a well-balanced scheme, i.e., a scheme which exactly preserves a discrete version of the relevant steady states. Higher order of accuracy is obtained by employing suitable minmod, ENO and WENO reconstructions, based on the equilibrium variables, to construct a well-balanced scheme. The resulting high order well-balanced schemes are validated on a suite of numerical experiments involving complex magnetic fields. The schemes are observed to be robust and resolve the complex physics well.