Shock wave structure for generalized Burnett equations

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 ["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.