A new HLLD Riemann solver with Boris correction for reducing Alfv’en speed. (arXiv:1902.02810v1 [physics.comp-ph])

A new HLLD Riemann solver with Boris correction for reducing Alfv’en speed. (arXiv:1902.02810v1 [physics.comp-ph])
<a href="http://arxiv.org/find/physics/1/au:+Matsumoto_T/0/1/0/all/0/1">Tomoaki Matsumoto</a>, <a href="http://arxiv.org/find/physics/1/au:+Miyoshi_T/0/1/0/all/0/1">Takahiro Miyoshi</a>, <a href="http://arxiv.org/find/physics/1/au:+Takasao_S/0/1/0/all/0/1">Shinsuke Takasao</a>

A new Riemann solver is presented for the ideal magnetohydrodynamics (MHD)
equations with the so-called Boris correction. The Boris correction is applied
to reduce wave speeds, avoiding an extremely small timestep in MHD simulations.
The proposed Riemann solver, Boris-HLLD, is based on the HLLD solver. As done
by the original HLLD solver, (1) the Boris-HLLD solver has four intermediate
states in the Riemann fan when left and right states are given, (2) it resolves
the contact discontinuity, Alfv’en waves, and fast waves, and (3) it satisfies
all the jump conditions across shock waves and discontinuities except for slow
shock waves. The results of a shock tube problem indicate that the scheme with
the Boris-HLLD solver captures contact discontinuities sharply and shock waves
without any overshoot when using the minmod limiter. The stability tests show
that the scheme is stable when $|u| lesssim 0.5c$ for a low Alfv’en speed
($V_A lesssim c$), where $u$, $c$, and $V_A$ denote the gas velocity, speed of
light, and Alfv’en speed, respectively. For a high Alfv’en speed ($V_A
gtrsim c$), where the plasma beta is relatively low in many cases, the stable
region is large, $|u| lesssim (0.6-1) c$. We discuss the effect of the Boris
correction on physical quantities using several test problems. The Boris-HLLD
scheme can be useful for problems with supersonic flows in which regions with a
very low plasma beta appear in the computational domain.

A new Riemann solver is presented for the ideal magnetohydrodynamics (MHD)
equations with the so-called Boris correction. The Boris correction is applied
to reduce wave speeds, avoiding an extremely small timestep in MHD simulations.
The proposed Riemann solver, Boris-HLLD, is based on the HLLD solver. As done
by the original HLLD solver, (1) the Boris-HLLD solver has four intermediate
states in the Riemann fan when left and right states are given, (2) it resolves
the contact discontinuity, Alfv’en waves, and fast waves, and (3) it satisfies
all the jump conditions across shock waves and discontinuities except for slow
shock waves. The results of a shock tube problem indicate that the scheme with
the Boris-HLLD solver captures contact discontinuities sharply and shock waves
without any overshoot when using the minmod limiter. The stability tests show
that the scheme is stable when $|u| lesssim 0.5c$ for a low Alfv’en speed
($V_A lesssim c$), where $u$, $c$, and $V_A$ denote the gas velocity, speed of
light, and Alfv’en speed, respectively. For a high Alfv’en speed ($V_A
gtrsim c$), where the plasma beta is relatively low in many cases, the stable
region is large, $|u| lesssim (0.6-1) c$. We discuss the effect of the Boris
correction on physical quantities using several test problems. The Boris-HLLD
scheme can be useful for problems with supersonic flows in which regions with a
very low plasma beta appear in the computational domain.

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