The HLLD Approximate Riemann Solver for Magnetospheric Simulation

A magnetohydrodynamic (MHD) algorithm for global simulations of planetary magnetospheres is developed based on an approximate nonlinear Riemann solver, the so-called Harten-Lax-van Leer-Discontinuities (HLLD) approximate Riemann solver. An approximate nonlinear solution of the MHD Riemann problem, in which the contributions of the background potential magnetic field are subtracted and multispecies plasmas as well as general equation of state are included, can be algebraically obtained under the assumptions that the normal velocity and the background potential magnetic field in the Riemann fan are constant. The theoretical aspects of the HLLD approximate Riemann solver are focused on, in particular.