Revised USM3D-ME Implementation of Negative Version of Spalart–Allmaras Turbulence Model

Since its publication in 2012, the negative version (SA-neg) of the Spalart–Allmaras model has been widely used to improve the iterative convergence of Reynolds-averaged Navier–Stokes solutions for practical turbulent flows. The success of this version is based on the rigorously proved positivity of the diffusion coefficient in the SA-neg partial differential equation and the corresponding positivity and boundedness of the continuous solution. However, some implementations of the SA-neg version in finite-volume computational fluid dynamics solvers may violate the positivity of discrete diffusion coefficients and result in the divergence of iterative solutions. A revised diffusion-based implementation of the SA-neg version has been accomplished in NASA’s cell-centered finite-volume flow solver, USM3D-ME. The implementation guarantees the positivity of discrete diffusion coefficients. This paper presents theoretical foundations for the revised implementation of the SA-neg version. Iterative convergence for different SA-neg implementations is studied for representative grids and flow conditions. With the revised implementation, fast iterative convergence to machine zero residuals is demonstrated for the test cases considered in the seventh AIAA Drag Prediction Workshop, held in 2022. Additionally, the robustness of the revised diffusion-based implementation is demonstrated for different discretization schemes, nonlinear iterative solvers, and turbulence models.