Steady Turbulent Flow Computations Using a Low Mach Fully Compressible Scheme

A recently proposed modification to fully compressible schemes significantly improves the resolution of low-Mach-number features, tackling the problem of excessive numerical dissipation as the Mach number reduces. This paper explores the application of this modification to Reynolds-averaged Navier–Stokes simulations using second- and fifth-order in-space schemes. Following verification of the modeling approach, four test cases are employed to highlight the scheme performance, including a backward-facing step, a two-dimensional lid-driven cavity, the NACA 4412 airfoil (incorporating a trailing-edge separation), and finally a Mach 2.25 oblique shock-wave–boundary-layer interaction. It demonstrates first that the converged solution is grid- and scheme-independent, as expected, and that the low-Mach-number correction provides a significant improvement in low-Mach-number regions. Because this correction is easy to implement, computationally inexpensive, and stable, the conclusion is that it should be recommended for all existing Godunov-type Reynolds-averaged Navier–Stokes solvers.