to be 5.0 and the gas to be ideal and monatomic. A normal shock wave forms ahead of the piston, the gas temperature Before a hybrid scheme can be developed combining the direct simulation Monte Carlo (DSMC) method and a Navier-Stokes (NS) (dashed curve) rises behind the shock and then falls as a representation, one must have access to compatible kinetic-split result of the cold piston surface (located at x/L ϭ 1).
fluxes from the NS portion of the hybrid scheme. The kinetic theory Because of the nearly constant pressure between the shock basis is given for the development of the required fluxes from the and the piston, the density (solid curve) rises in the thermal Chapman-Enskog velocity distribution function for a simple gas;
layer in an inverse ratio to the temperature. In this case, and these are then extended to a polyatomic gas by use of the Eucken approximation. The derived fluxes are then used to imple-the peak density is 8.2 times the density behind the shock ment boundary conditions at solid surfaces that are based on conwave. Although the DSMC method must be used to obtain cepts associated with kinetic theory and the DSMC method. This the proper shock wave profile, as is well known, it is clear approach is shown to lead to temperature slip and velocity slip as that the much higher density in the thermal layer would a natural outcome of the new formulation, a requirement for use lead to a greatly increased DSMC simulation cost in that in the near-continuum regime where DSMC and NS must be joined. Several different flows, for which solid boundaries are not present, region, prompting consideration of a hybrid scheme, where are computed using the derived fluxes, together with a secondthe DSMC method would be used to model the outer flow order finite-volume scheme, and the results are shown to agree and the NS equations to model the thermal layer. This well with several established numerical schemes for the NS concept is schematically depicted in Fig. 2.
equations.