Minimal models for shock fronts in rarefied gases: From kinematics to thermodynamics

The effect of interparticle collisions on a 'kinematic' shock wave produced by a velocity gradient in a cold atomic gas (Ar) is studied, to the end of establishing a connection between such kinematic shocks and the 'traditional' fluid dynamic shock front. This last, being produced by a gradient in the speed of sound c, requires a sufficient degree of translational equilibrium to charge the formula c = (?KT/m) Of a definite meaning. In order to include the collisional effects we use both a DSMC (Direct Simulation Monte Carlo) model and a Monte Carlo (MC) implementation of the relaxation (BGK) collision term, where the characteristic frequency ? in the relaxation term is set equal to the equilibrium interparticle collision frequency, the latter being a local function of the particle density, n, and the static temperature, T, only. The substantial equality of DSMC and BGK/MC results for a sufficiently high value of the initial density n proves that the kinematic and thermodynamic descriptions of the shock front can be smoothly joined by scaling this parameter. The results reported suggest that the intermediate regime, where a fundamentally kinematic shock is affected by few collision events, provides a solid ground to study the non equilibrium kinetics of reactive shock fronts. © 200J by D.Bruno.