Calculation of Gas Diffusion at a Contact Discontinuity by the Godunov–Kolgan Method

Abstract

It has previously been shown that the generalized Godunov–Kolgan scheme, unlike the Kolgan scheme, is able to exclude physically meaningless solutions in the numerical integration of the Euler equations for an inviscid gas and is easily adapted for calculation of single-component viscous gas flows. This paper proposes a modification to the generalized scheme for modeling viscous multicomponent gas flows based on the Navier–Stokes equations. To test the scheme, the problem of gas diffusion on a flat contact discontinuity is solved. We demonstrate the possibility of calculating diffusion flows and gas composition based on average, rather than minimum, concentration gradients within the computational cell. The proposed approach is more universal, easy to implement, and most importantly, it preserves the monotonicity of the solution and provides the second order of approximation in space on smooth solutions for all gas parameters, including component composition. A calculation with a frozen component composition within the calculation cell yields a first-order solution for the gas composition; however, for this problem its results are almost indistinguishable in terms of concentrations and similar for other gas parameters.