Riemann Problem and Elementary Wave Interactions for a Simplified Magnetic Fluid Model

Abstract

In the present paper, we mainly studied the Riemann problem and wave interaction of a simplified magnetohydrodynamic equation system. Due to the complex Riemann problem and wave interactions in the magnetohydrodynamic equations, most previous studies either did not investigate the interaction of elementary waves or, if they did, lacked supporting numerical experiments. This paper simplifies the magnetohydrodynamic equations using variable substitution. Using the characteristic line method to solve the Riemann problem and elementary wave interaction of the simplified magnetohydrodynamic equations, the form of the solution is more symmetrical and the interaction between waves has also become more regular. The correctness of the results was verified by numerical experiments.

Keywords

• magnetohydrodynamic equation
• Riemann problem
• wave interaction