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A conservative pressure‐correction method for the Euler and ideal MHD equations at all speeds
Author(s) -
van der Heul D. R.,
Vuik C.,
Wesseling P.
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.322
Subject(s) - mach number , magnetohydrodynamics , discretization , euler equations , compressibility , magnetohydrodynamic drive , compressible flow , euler's formula , physics , flow (mathematics) , mechanics , mathematics , magnetic field , classical mechanics , mathematical analysis , quantum mechanics
To 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.