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Non-oscillatory relaxation schemes for one-dimensional ideal magnetohydrodynamic equations

2009; Elsevier BV; Volume: 10; Issue: 6 Linguagem: Inglês

10.1016/j.nonrwa.2008.09.024

1878-5719

Mapundi K. Banda,

Advanced Mathematical Physics Problems

We present a high-order accurate relaxed non-oscillatory scheme for solving magnetohydrodynamic (MHD) equations. The computations reported here demonstrate the remarkable simplicity and versatility of semi-discrete relaxation schemes as solvers for ideal MHD equations. Simulations will be presented for two prototype MHD problems, the one-dimensional Brio–Wu shock tube problems. A qualitative comparison reveals an excellent agreement with previous results based on other approaches. Furthermore, the numerical results demonstrate that such semi-discrete schemes preserve the ∇⋅B=0 constraint without necessarily needing the constrained-transport enforcement.