Abstract
Stationary shock wave solutions for the generalized Burnett equations (GBE) [A. V. Bobylev, “Generalized Burnett hydrodynamics,” J. Stat. Phys. 132, 569 (2008)] are studied. Based on the results of Bisi et al. [“Qualitative analysis of the generalized Burnett equations and applications to half-space problems,” Kinet. Relat. Models 1, 295 (2008)], we choose a unique (optimal) form of GBE and solve numerically the shock wave problem for various Mach numbers. The results are compared with the numerical solutions of Navier–Stokes equations and with the Mott–Smith approximation for the Boltzmann equation (all calculations are done for Maxwell molecules) since it is believed that the Mott–Smith approximation yields better results for strong shocks. The comparison shows that GBE yield certain improvement of the Navier–Stokes results for moderate Mach numbers.
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