A low-dissipation HLLD approximate Riemann solver for a very wide range of Mach numbers

We propose a new Harten-Lax-van Leer discontinuities (HLLD) approximate Riemann solver to improve the stability of shocks and accuracy low-speed flows in multidimensional magnetohydrodynamic (MHD) simulations. Stringent benchmark tests verify that is more robust against numerical shock instability accurate for low-speed, nearly incompressible than original solver, whereas additional computational costs are quite low. The novel ability enables us tackle MHD systems, including both high low Mach number flows.