  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 it exhibits
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.
