**Topic/Type**:
2.1 MHD, EHD & other fluid methods, Poster

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The HLLD approximate Riemann solver for magnetospheric simulations

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T. Miyoshi**^{1}, N. Terada^{2}, Y. Matsumoto^{3}, K. Fukazawa^{4}, T. Umeda^{3}, K. Kusano^{3}

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*^{1} Hiroshima University, Higashi-hiroshima, Japan

^{2} Tohoku University, Sendai, Japan

^{3} Nagoya University, Nagoya, Japan

^{4} Kyusyu University, Fukuoka, Japan

A high resolution magnetohydrodynamic (MHD) simulation code appropriate for magnetospheric simulations is developed based on Harten-Lax-van Leer-Discontinuities (HLLD) approximate Riemann solver [Miyoshi and Kusano, 2005].

In the present code, a strong background potential magnetic field is algebraically removed from the conservative variables of the MHD equations in order to suppress large numerical errors due to rapid variations of the strong background field [Tanaka, 1994]. Despite the nonlinearity of the HLLD solver, we can algebraically obtain the internal states of the HLLD solver.

Multispecies plasmas and an arbitrary equation of state can also be incorporated in the present code. It is theoretically shown that the positivity of densities and internal energies is preserved in one-dimension if local maximum and minimum characteristic speeds are adequately given.

Moreover, the HLLD solver is applied for the conservative {\it Boris correction} MHD equations [Gombosi, et al., 2002], where an effective mass is added only to the momentum in the conservative variables in proportion to the square of the advection speed. We successfully derive the HLLD internal states for the {\it Boris correction} MHD equations and can reduce CPU time to obtain high-resolution steady-state solutions.

The present extended HLLD code can be straightforwardly introduced in existing codes by conservative schemes and can become a superior alternative in the viewpoint of resolution, robustness, and efficiency.