A conservative pressure‐correction method for the Euler and ideal MHD equations at all speeds

Abstract

AbstractTo efficiently compute weakly compressible magnetohydrodynamic flows in astrophysical applications, approximate low Mach number reduced forms of the compressible MHD equations are frequently used. This is because standard characteristic‐based schemes for the full compressible MHD equations are inefficient and inaccurate for computing low Mach number magnetohydrodynamic flow, as a result of the increasing stiffness and weakening pressure/density coupling of the equations when M ↓ 0. Furthermore, these schemes are colocated, so that additional and artificial measures have to be taken to ensure solenoidality of the magnetic field. We present a new method with a staggered spatial discretization and a pressure‐correction solution algorithm that is more suitable for computing weakly compressible MHD flow, because of its Mach‐uniformity and efficient and accurate handling of the solenoidality constraint on the magnetic field. Copyright © 2002 John Wiley & Sons, Ltd.