  We study the classical problem of planar shock refraction at an oblique
density discontinuity, separating two gases at rest. When the shock impinges on
the density discontinuity, it refracts and in the hydrodynamical case 3 signals
arise. Regular refraction means that these signals meet at a single point,
called the triple point.
  After reflection from the top wall, the contact discontinuity becomes
unstable due to local Kelvin-Helmholtz instability, causing the contact surface
to roll up and develop the Richtmyer-Meshkov instability. We present an exact
Riemann solver based solution strategy to describe the initial self similar
refraction phase, by which we can quantify the vorticity deposited on the
contact interface. We investigate the effect of a perpendicular magnetic field
and quantify how addition of a perpendicular magnetic field increases the
deposition of vorticity on the contact interface slightly under constant Atwood
number. We predict wave pattern transitions, in agreement with experiments, von
Neumann shock refraction theory, and numerical simulations performed with the
grid-adaptive code AMRVAC. These simulations also describe the later phase of
the Richtmyer-Meshkov instability.
