A kinetic energy and entropy preserving scheme for compressible magnetohydrodynamics

Abstract

This paper extends the kinetic energy and entropy preserving (KEEP) scheme, which was originally designed for compressible fluid dynamics, to include compressible magnetohydrodynamics (MHD). In MHD, the magnetic energy included in the total energy equation is consistent with that derived from the induction equation. Discretizing the spatial derivative in the induction equation using the central finite difference preserves the solenoidal constraint of the magnetic field. Numerical fluxes for the momentum and the total energy related to the magnetic field can be derived for the momentum and total energy from the Lorentz force and the solenoidal constraint, even in discrete form. Numerical results confirm that the KEEP scheme enables non-dissipative and stable MHD simulations, unlike the conventional central difference method.