Maintaining pressure positivity in magnetohydrodynamic simulations

Higher order Godunov schemes for solving the equations of magnetohydrodynam ics (MHD) have recently become available. Because such schemes update the t otal energy, the pressure is a derived variable. In several problems in lab oratory physics, magnetospheric physics, and astrophysics the pressure can be several orders of magnitude smaller than either the kinetic energy or th e magnetic energy. Thus small discretization errors in the total energy can produce situations where the gas pressure can become negative. In this pap er we design a linearized Riemann solver that works directly on the entropy density equation. We also design switches that allow us to use such a Riem ann solver safely in conjunction with a normal Riemann solver for MHD. This allows us to reduce the discretization errors in the evaluation of the pre ssure variable. As a result we formulate strategies that maintain the posit ivity of pressure in all circumstances. We also show via test problems that the strategies designedhere work. (C) 1999 Academic Press.