Towards calculating turbulent flows with the Spalart–Allmaras model by using the LU-SGS-GMRES algorithm

A numerical model for turbulent three-dimensional flows at high Reynolds numbers is considered. The RANS approach based on the turbulence model of Spalart and Allmaras (SA) is used. The method of wall functions for modeling surface friction is implemented. Specifics of the numerical algorithm based on the LU-SGS–GMRES solver, and program implementation of the present numerical model are discussed. Numerical solutions of the compressible viscous gas flow over a flat plate and in an asymmetric diffuser, and also mathematical modeling of the turbulent mixture layer of two compressible flows are carried out to perform verification and validation of the RANS equations with the SA model for turbulence and the method of wall functions for modeling boundary conditions of the “law of wall” type.