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A new Riemann solver is presented for the ideal magnetohydrodynamics (MHD)equations with the so-called Boris correction. The Boris correction is appliedto reduce wave speeds, avoiding an extremely small timestep in MHD simulations.The proposed Riemann solver, Boris-HLLD, is based on the HLLD solver. As doneby the original HLLD solver, (1) the Boris-HLLD solver has four intermediatestates in the Riemann fan when left and right states are given, (2) it resolvesthe contact discontinuity, Alfv\'en waves, and fast waves, and (3) it satisfiesall the jump conditions across shock waves and discontinuities except for slowshock waves. The results of a shock tube problem indicate that the scheme withthe Boris-HLLD solver captures contact discontinuities sharply and it exhibitsshock waves without any overshoot when using the minmod limiter. The stabilitytests show that the scheme is stable when $|u| \lesssim 0.5c$ for a lowAlfv\'en speed ($V_A \lesssim c$), where $u$, $c$, and $V_A$ denote the gasvelocity, speed of light, and Alfv\'en speed, respectively. For a high Alfv\'enspeed ($V_A \gtrsim c$), 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 ofthe Boris correction on physical quantities using several test problems. TheBoris-HLLD scheme can be useful for problems with supersonic flows in whichregions with a very low plasma beta appear in the computational domain.

A new HLLD Riemann solver with Boris correction for reducing Alfv\'en speed