MHD simple waves and the divergence wave

Abstract

In this paper we investigate magnetohydrodynamic (MHD) simple divergence waves in MHD, for models in which ∇⋅B≠0. These models are related to the eight wave Riemann solvers in numerical MHD, in which the eighth wave is the divergence wave associated with ∇⋅B≠0. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function φ. We consider the form of the MHD equations used by both Powell et al. [1] and Janhunen [2]. It is shown that the Janhunen version of the equations possesses fully nonlinear, exact simple wave solutions for the divergence wave, but no physically meaningful simple divergence wave solution exists for the Powell et al. system. We suggest that the 1D simple, divergence wave solution for the Janhunen system, may be useful for the testing and validation of numerical MHD codes.