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In order to test the gas-kinetic based hydrodynamic scheme given in paper I (K. H. Prendergast and K. Xu, J. Comput. Phys.109, 53, 1993) as a Navier-Stokes solver, we extend the scheme to two dimensions and exhibit some Navier-Stokes solutions. The scheme is a high-resolution gas kinetic scheme in both space and time. The advective and diffusive fluxes are coupled and solved at the same time by following the time-dependent velocity distribution function for particles. Numerical results for some well-defined Euler and Navier-Stokes test cases are presented. The Kolmogorov and the laminar boundary layer problems exhibit the dominance of the real viscosity effects. The strong shock interaction test cases show the applicability of the scheme to supersonic gas flow.
Xu et al. (Thu,) studied this question.