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Keywords:

  • finite volume;
  • compressible flow;
  • AUSM;
  • PISO;
  • MHD;
  • all Mach

SUMMARY

In this paper, we propose an extension of a PISO method, previously developed to solve the Euler equations, and which is here extended to the ideal magnetohydrodynamic (MHD) equations. By following a pressure-based approach, we make use of the flexibility given by pressure equation for calculating flows at arbitrary Mach numbers. To handle MHD discontinuities, we have adapted the MHD-Advection Upstream Splitting Method for our pressure-based formulation. With the purpose of validation, four sets of test cases are presented and discussed. We start with the circularly polarized Alfvén waves that serves as a smooth flow validation. The second case is the 1-D Riemann problem that is calculated using both 1-D and 2-D formulation of the MHD equations. The third and fourth problems are the Orszag–Tang vortex and the supersonic low- β cylinder allowing validation of the method in complex 2-D MHD shock interaction. Copyright © 2013 John Wiley & Sons, Ltd.