Tetrahedral Unstructured Navier-Stokes Method for Turbulent Flows

Abstract

A method is presented for solving the Navier-Stokes equations for turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered, finite volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of the skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer and for the ONERA M6 wing under a high-Reynolds-number, transonic, separated flow condition