Approximate solutions for the structure of shock waves

Abstract

Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness δ_n. A detailed error analysis provides explanations for this result. An asymptotic analysis of δ_n for large Mach numbers shows that it scales with the Maxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.