Numerical investigation of Richtmyer–Meshkov instability in shock-driven light square bubble via magnetohydrodynamics

Abstract

This study presents a numerical investigation of magnetohydrodynamics (MHD) instability in a shock-driven light square bubble, examining the complex interactions at the interface between shocked fluids in the presence of a magnetic field. By incorporating magnetic fields, the dynamics of such instabilities become even more complex, leading to novel behavior in terms of vorticity deposition, mixing, and interface morphology. For numerical simulation, an unsteady compressible ideal magnetohydrodynamics equations in two-dimensional space is solved with the corner transport upwind ＋ constrained transport schemes while preserving the magnetic field’s divergence-free condition. The numerical results show good agreement with the available hydrodynamics experimental data and magnetohydrodynamics calculations. The research results demonstrate that the transverse magnetic field plays a crucial role in the development of MHD-RMI in a light square bubble driven by a planar shock wave. It significantly affects the flow field structure, leading to changes in interface morphology, shock wave structure, vortices and enstrophy. The baroclinic torque induced by magnetic tension at the interface counteracts the torque from velocity shear, thereby inhibiting the roll of Kelvin–Helmholtz vortex. A comprehensive analysis of some physical quantities, including magnetic energy, magnetic strength, and magnetic tension on the square bubble, is presented. MHD-RMI has been found to be a highly effective mechanism for enhancing the magnetic field, thereby improving the suppression of flow instability. Finally, a detailed analysis of the impact of the magnetic field on the time evolution of the interface features is conducted.