Finite Volume Methods for Wave Propagation in Stratified Magneto-Atmospheres

Abstract

We present a model for simulating wave propagation in stratified magneto-atmospheres. The model is based on equations of ideal MHD together with gravitational source terms. In addition, we present suitable boundary data and steady states to model wave propagation. A finite volume framework is developed to simulate the waves. The framework is based on HLL and Roe type approximate Riemann solvers for numerical fluxes, a positivity preserving fractional steps method for discretizing the source and modified characteristic and Neumann type numerical boundary conditions. Second-order spatial and temporal accuracy is obtained by using an ENO piecewise linear reconstruction and a stability preserving Runge-Kutta method respectively. The boundary closures are suitably modified to ensure mass balance. The numerical framework is tested on a variety of test problems both for hydrodynamic as well as magnetohydrodynamic configurations. It is observed that only suitable choices of HLL solvers for the numerical fluxes and balanced Neumann type boundary closures yield stable results for numerical wave propagation in the presence of complex magnetic fields.