A 2ND-ORDER DESCRIPTION OF SHOCK STRUCTURE

The structure of gas-dynamic shock waves is of interest in hypersonic flow studies and also constitutes a straightforward test for competing kinetic theories. The description of the shock profiles may be obtain ed from a second-order theory in the Knudsen number. The BGK approxima tion to the Boltzmann equation introduces additional terms in the tran sport of momentum and energy. These relations, known as the Burnett eq uations, improve the agreement between calculated shock profiles and e xperiment. However, for some formulations of these equations, the solu tion breaks down at a critical Mach number. In addition, certain terms in the Burnett equations allow unphysical effects in gas flow. A modi fied kinetic theory has been proposed by Woods (An Introduction to the Kinetic Theory of Gases and Magnetoplasmas, Oxford Univ. Press, Oxfor d, 1993) which eliminates the frame dependence of the standard kinetic theory and corrects some of the second-order terms. This article desc ribes a novel method devised to solve the time-independent conservatio n equations, including the second-order terms. The method is used to s olve the shock structure problem in one dimension. It is based on a fi nite difference global scheme (FDGS), in which a Newton procedure is a pplied to a discretized version of the governing equations and boundar y conditions. The method is first applied to the Navier-Stokes formula tion of the shock equations. It is then successfully used to integrate a modified version of the second-order equations derived by Woods for monatomic gases, up to a Mach number of 30. Results of the calculatio ns a re compared with experimental data for Argon gas flows characteri zed by upstream Mach numbers up to 10. The agreement is good, well wit hin the data point spread. The FDGS method converges rapidly and it ma y be used to study other problems of the same general nature. (C) 1995 Academic Press, Inc.