The HLLD Riemann solver based on magnetic field decomposition method for the numerical simulation of magneto-hydrodynamics

By splitting magnetic field into two components (internal plus external), we derived an extended formulation of the HLLD Riemann solver for numerical simulation of magnetohydrodynamics (MHD). This new solver is backward compatible with the standard HLLD Riemann solver when the external component of the magnetic field is zero. Moreover, the solver is more robust than the standard HLLD solver in applications to low plasma β (the ratio between thermal and magnetic pressures) cases, where the thermal pressure may become negative from subtracting the kinetic and large magnetic energy from the large total energy density in a Godunov type numerical scheme. Our numerical tests show that the extended HLLD solver works well for the cases of magnetic field decomposition, and maintains high resolution similar to the standard HLLD.