On the computation of compressible turbulent flows on unstructured grids

An accurate, fast, matrix-free implicit method has been developed to solve Compressible turbulent flow problems using the Spalart and Allmaras one equ ation turbulence model on unstructured meshes. The mean-flow and turbulence -model equations are decoupled in the time integration in order to facilita te the incorporation of different turbulence models and reduce memory requi rements. Both mean flow and turbulent equations are integrated in time usin g a linearized implicit scheme. A recently developed, fast, matrix-free imp licit method, GMRES + LU-SGS, is then applied to solve the resultant system of linear equations. The spatial discretization is carried out using a hyb rid finite volume and finite element method, where the finite volume approx imation based on a containment dual control volume rather than the more pop ular median-dual control volume is used to discretize the inviscid fluxes, and the finite element approximation is used to evaluate the viscous flux t erms. The developed method is used to compute a variety of turbulent flow p roblems in both 2D and 3D. The results obtained are in good agreement with theoretical and experimental data and indicate that the present method prov ides an accurate, fast, and robust algorithm for computing compressible tur bulent flows on unstructured meshes.