Abstract
A fourth-order modified Runge-Kutta scheme augmented with TVD models have been developed to solve the ideal two-dimensional MHD equations. The numerical scheme is applied to supersonic flow within a channel including compression and expansion corners in the current investigation. The flowfield includes oblique shocks, expansion waves, shock reflections, shock/expansion interactions, and secondary wave patterns due to magnetic field. The solutions are compared to analytical solutions when available. The numerical scheme is shown to be accurate with ability to capture physical phenomena occurring in the flowfield without any or with minimum oscillations in the solution.
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