Semirelativistic Magnetohydrodynamics and Physics-Based Convergence Acceleration

We derive a system of equations for semirelativistic magnetohydrodynamics (MHD) in which the bulk speed and the sound speed of the plasma are nonrelativistic, but the Alfvén speed can be relativistic. The characteristic wave speeds of the modified equation set are determined and compared to the wave speeds in “classical” (MHD). The stability conditions of the semirelativistic MHD equations are also investigated in detail. orm of the MHD equations has a use beyond modeling flows with high Alfvén speeds. Even in cases with moderate Alfvén speeds, the semirelativistic form or certain approximations of it can be used to achieve accelerated numerical convergence to steady-state solutions by artificially reducing the speed of light, provided that the steady-state solutions of these equations are fully independent of the speed of light. Numerical tests are presented that demonstrate the behavior of solutions at high Alfvén speeds and the convergence acceleration that can be achieved when a steady-state solution is desired.