We report numerical results of the linear growth of the Richtmyer-Meshkov instability (RMI) in compressible fluids and in the presence of a magnetic field. These results are obtained with the Lagrangian code LPC-MHD in which media are supposed to be compressible ideal gases. We first applied a magnetic field perpendicular to the wave vector and perpendicular to the shock wave propagation and observed no changes on the perturbation growth velocity compared to the case without magnetic field. We also considered the configuration where the magnetic field is parallel to the wave vector. We observed the stabilization of the instability with oscillations of the perturbations amplitude. Numerical results are compared to impulsive acceleration model of the RMI in the presence of a transverse magnetic field, in the non-compressible limit. A good agreement is obtained between numerical results and model for both the amplitude and the frequency of oscillations. Compressibility seems to have negligible effects.
