A low-diffusion flux-splitting scheme for Navier-Stokes calculations

Abstract

The development of a new flux-splitting approach for perfect-gas reacting-gas Navier-Stokes computations is presented in this work. Three distinct variants are proposed, each of which is designed to capture a stationary contact discontinuity without excess numerical diffusion while providing a monotone resolution of strong normal shock waves. The variants differ in their resolution of strong oblique shock waves and in their performance for unsteady flow situations. A straightforward extension of the methods to general flows in thermo-chemical non-equilibrium is also proposed, and the construction of robust approximate linearizations of the schemes is discussed. Comparisons of the new splittings with other upwinding techniques are presented for four steady-state test cases: Mach 8 viscous flow over a 15 ° wedge (perfect gas), Mach 6 viscous flow over a cone-flare configuration (perfect gas), Mach 16 viscous flow over a cylinder (five-species reacting-air), and a subsonic reacting shear layer (seven-species hydrogen-air chemistry). Shock tube simulations are also performed to ascertain the effectiveness of the schemes for unsteady flow situations. It is shown that the new methods combine the desirable traits of more sophisticated Godunov-type schemes in the resolution of discontinuities with the robustness and simplicity of flux-vector splittings.