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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