Higher-order aerodynamic numerical simulations in compressible RANS framework with inverse-ω scale variable

Abstract

The use of higher-order methods to robustly compute turbulent flows governed by the multi-equation turbulence model in Reynolds-averaged Navier-Stokes (RANS) framework is a challenging topic in the computational fluid dynamics (CFD) community. In this paper, we propose two aspects of measures involving the physical model and the numerical scheme. Firstly, a λ-scale (=1/ωn) is derived instead of the well-known ω in SSG/LRR Reynolds-stress model (RSM) and SST eddy viscosity model (EVM) due to its natural boundary conditions for viscous walls and help to the positivity preservation of dissipation rate ε in turbulence equations when n=1/(2m),m=1,2,3.... Secondly, a geometric-conservation-preservation negativity-correction (GCPNC) method is proposed on the implicit time integration procedure with right-hand-side (RHS) term discretized by high-order weighted compact nonlinear schemes (WCNSs). It can guarantee the positivity of normal Reynolds stresses or turbulent kinetic energy. Numerical tests with real-life compressible flows are reported to demonstrate the robustness and accuracy of the present methods. Relevant cases include the supersonic square duct flow, the flows over delta wing, wing-body configuration and high-lift configuration.