Maintaining pressure positivity in magnetohydrodynamic simulations. (English) Zbl 0930.76050

Summary: Higher order Godunov schemes for solving the equations of magnetohydrodynamics (MHD) have recently become available. Because such schemes update the total energy, the pressure is a derived variable. In several problems in laboratory physics, magnetospheric physics, and astrophysics the pressure can be several orders of magnitude smaller than either the kinetic energy or the magnetic energy. Thus small discretization errors in the total energy can produce situations where the gas pressure can become negative. In this paper 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 Riemann solver safely in conjunction with a normal Riemann solver for MHD. This allows us to reduce the discretization errors in the evaluation of the pressure variable. As a result, we formulate strategies that maintain the positivity of pressure in all circumstances. We also show via test problems that the strategies designed here work.


76M20 Finite difference methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] Ryu, D.; Ostriker, J. P.; Kang, H.; Cen, R., Ap. J., 414, 1 (1993)
[3] vanLeer, B., J. Comput. Phys., 32, 101 (1979)
[4] Roe, P. L.; Balsara, D. S., SIAM J. Appl. Math., 56, 57 (1996)
[5] Harten, A.; Hyman, J., J. Comput. Phys., 50, 235 (1983)
[6] Roe, P. E., J. Comput. Phys., 53, 357 (1981)
[7] Balsara, D. S., Ap. J. Supp., 116, 119 (1998)
[8] Balsara, D. S., Ap. J. Supp., 116, 133 (1998)
[9] Bell, J. B.; Colella, P.; Trangenstein, J. A., J. Comput. Phys., 82, 362 (1989)
[10] Einfeldt, B.; Munz, C. D.; Roe, P. L.; Sjogreen, B., J. Comput. Phys., 92, 273 (1991)
[11] Shu, C. W.; Osher, S., J. Comput. Phys., 87, 439 (1989)
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