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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 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, Alfven 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 Alfven speed ($V_A lesssim c$), where $u$, $c$, and $V_A$ denote the gas velocity, speed of light, and Alfven speed, respectively. For a high Alfven 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 simple form of the Boris solver in particle-in-cell (PIC) simulation is proposed. It employs an exact solution of the Lorentz-force part, and it is equivalent to the Boris solver with a gyrophase correction. As a favorable property for stable schem
Convection is an important physical process in astrophysics well-studied using numerical simulations under the Boussinesq and/or anelastic approximations. However these approaches reach their limits when compressible effects are important in the high
We construct Boris-type schemes for integrating the motion of charged particles in particle-in-cell (PIC) simulation. The new solvers virtually combine the 2-step Boris procedure arbitrary n times in the Lorentz-force part, and therefore we call them
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