Two-dimensional MHD solver by fluctuation splitting and dual time stepping

Abstract

Numerical solutions of 2D magneto-hydrodynamic (MHD) equations by means of a fluctuation splitting (FS) scheme (with a new wave model and dual time stepping technique) is presented. The FS scheme, essentially based on the model explained in Proceedings of the Tenth International Conference, vol. 10, Swansea, 21-25 July 1997; Godunov Symposium, University of Michigan, Ann Arbor, 1-2 May 1997; Physics Symposium, Alanya, Turkey, 27-31 October 1998; J. Comput. Phys. 1999; 153:437-466; Ph.D. Thesis, University of Marmara, Istanbul, Turkey, 2000), was extended to include gravitational source effects, limiters to limit oscillations, high order time accuracy through multistage Runge-Kutta steps, and a dual time stepping scheme to drive magnetic field divergence to zero during iterations. The numerical results show that with the new wave model called MHD-B along with its embedded numerical dissipation, correct limiting viscosity solution has been recovered and that it can safely be used in order to investigate steady or time dependent magnetized or neutral compressible flows in two dimensions. Copyright (c) 2006 John Wiley & Sons, Ltd.