High-Order Numerical Method for Magnetohydrodynamic Control of Shock-Induced Separation

Abstract

Magnetic fields significantly affect the flow of ionized gases and may be exploited for the control of separation, transition, and turbulence. The wave structure of ionized gas high-speed flows under the influence of magnetic fields is more involved than the waves of ordinary gas dynamics and high-resolution is required to accurately compute the complex wave interactions of such flows with discontinuities. Numerical solutions of the nonlinear ideal and viscous magnetohydrodynamic equations are obtained with a high-order-accurate shock-capturing scheme. The numerical method is tested for flows containing strong magnetohydrodynamic discontinuities and smooth flow features to ensure that it maintains high-order accuracy for the smooth parts of the flow, it preserves numerical stability, and eliminates nonphysical features that result from the violation of the divergence-free condition for the magnetic field. Problems with exact solutions, such as the convection of smooth waves caused by magnetic fields, are also solved numerically to validate the method. The numerical method is applied to simulate separation control at the interaction region of an oblique shock with a laminar boundary layer under the influence of magnetic fields.