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Due to the limited cell resolution in the representation of flow variables, apiecewise continuous initial reconstruction with discontinuous jump at a cellinterface is usually used in modern computational fluid dynamics methods.Starting from the discontinuity, a Riemann problem in the Godunov method issolved for the flux evaluation across the cell interface in a finite volumescheme. With the increasing of Mach number in the CFD simulations, theadaptation of the Riemann solver seems introduce intrinsically a mechanism todevelop instabilities in strong shock regions. Theoretically, the Riemannsolution of the Euler equations are based on the equilibrium assumption, whichmay not be valid in the non-equilibrium shock layer. In order to clarify theflow physics from a discontinuity, the unsteady flow behavior ofone-dimensional contact and shock wave is studied on a time scale of (0~10000)times of the particle collision time. In the study of the non-equilibrium flowbehavior from a discontinuity, the collision-less Boltzmann equation is firstused for the time scale within one particle collision time, then the directsimulation Monte Carlo (DSMC) method will be adapted to get the furtherevolution solution. The transition from the free particle transport to thedissipative Navier-Stokes (NS) solutions are obtained as an increasing of time.The exact Riemann solution becomes a limiting solution with infinite number ofparticle collisions. For the high Mach number flow simulations, the points inthe shock transition region, even though the region is enlarged numerically tothe mesh size, should be considered as the points inside a highlynon-equilibrium shock layer.

Valid Physical Processes from Numerical Discontinuities in Computational Fluid Dynamics