The velocity distribution function in an infinitely strong shock wave

The structure of an infinitely strong shock wave (i.e., a shock wave with i nfinitely large upstream Mach number) is investigated on the basis of the B oltzmann equation for hard-sphere molecules. The velocity distribution func tion is expressed as a sum of a multiple of the Dirac delta function, cente red at the upstream bulk velocity, and the remainder. The equation for the latter, which contains the linear collision term linearized around the delt a function and the nonlinear collision term, is solved numerically by an ac curate finite-difference method after the nonlinear collision term is repla ced by the BGK collision model. The result not only confirms the singularit y in the remainder observed in the previous Monte Carlo simulation [Cercign ani , Phys. Fluids 11, 2757 (1999)] but also provides more detailed informa tion about the structure of the singularity. (C) 2000 American Institute of Physics. [S1070-6631(00)00508-0].