Prendergast, Kevin H.; Xu, Kun Numerical hydrodynamics from gas-kinetic theory. (English) Zbl 0791.76059 J. Comput. Phys. 109, No. 1, 53-66 (1993). We present a new hydrodynamics code, based on the solution of the Bhatnagar-Gross-Krook model of the Boltzmann equation. The basic idea is to construct an approximate, locally valid solution of a set of nonlinear integral equations for the equilibrium Maxwell-Boltzmann distribution, and use this solution to solve the BGK equation for the velocity distribution function at cell walls. Our code appears to behave as well as current high-order difference schemes at shocks and to give better results for rarefaction waves. Cited in 6 ReviewsCited in 65 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 76L05 Shock waves and blast waves in fluid mechanics Keywords:Bhatnagar-Gross-Krook model; equilibrium Maxwell-Boltzmann distribution; velocity distribution function; rarefaction waves Software:HLLE PDFBibTeX XMLCite \textit{K. H. Prendergast} and \textit{K. Xu}, J. Comput. Phys. 109, No. 1, 53--66 (1993; Zbl 0791.76059) Full Text: DOI