Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

摘要

The paper presents two contributions in the context of numerical simulationof magnetized fluid dynamics. First, we show how to extend the idealmagnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergencecleaning mechanism in such a way that the resulting model is consistent withthe second law of thermodynamics. As a byproduct of these derivations, we showthat not all of the commonly used divergence cleaning extensions of the idealMHD equations are thermodynamically consistent. Secondly, we present anumerical scheme that mimics the behavior of the novel continuous system byconstructing a specific finite volume discretization that is consistent withthe discrete thermodynamic entropy and includes a mechanism to control thediscrete divergence error of the magnetic field by construction. We implementthe new MHD solver in the adaptive mesh refinement code FLASH where we comparethe divergence cleaning efficiency to the constrained transport solveravailable in FLASH (unsplit staggered mesh scheme).