Numerical analysis of Richtmyer–Meshkov instability of circular density interface in presence of transverse magnetic field

Abstract

Richtmyer–Meshkov instability (RMI) caused by the interaction of a shock wave and a density interface in the presence of a transverse magnetic field is investigated numerically using the ideal compressible magneto-hydro-dynamic (MHD) equations. The MHD equations are solved with the corner transport upwind + constrained transport algorithm that guarantees the divergence-free constraint on the magnetic field. The numerical results clearly capture the evolution of the density interface induced by the RMI for both HD and MHD situations, which are in good agreement with the previous experimental and numerical results. Moreover, current numerical results reveal a potential stabilizing mechanism of the flow instability by the transverse magnetic field: it is found that the magnetic tension produces a torque on the interface fluid, which is opposite to the torque driven by the velocity shear; therefore, the Kelvin–Helmholtz instability on the density interface caused by the velocity shear is effectively suppressed. In addition, detailed information about the magnetic strength, magnetic energy, magnetic tension, and vorticity on the density interface is also quantitatively analyzed, and the results suggest that the RMI is quite an efficient mechanism for the amplification of the magnetic field, which, in turn, enhances the suppression of the flow instability.