AN IMPLICIT MIXED FINITE-VOLUME-FINITE-ELEMENT METHOD FOR SOLVING 3D TURBULENT COMPRESSIBLE FLOWS

The development of new aeronautic projects require accurate and effici ent simulations of compressible flows in complex geometries. It is wel l known that most flows of interest are at least locally turbulent and that the modelling of this turbulence is critical for the reliability of the computations. A turbulence closure model which is both cheap a nd reasonably accurate is an essential part of a compressible code. An implicit algorithm to solve the 2D and 3D compressible Navier-Stokes equations on unstructured triangular/tetrahedral grids has been extend ed to turbulent flows. This numerical scheme is based on second-order finite element-finite volume discretization: the diffusive and source terms of the Navier-Stokes equations are computed using a finite eleme nt method, while the other terms are computed with a finite volume met hod. Finite volume cells are built around each node by means of the me dians. The convective fluxes are evaluated with the approximate Rieman n solver of Roe coupled with the van Albada limiter. The standard k-ep silon model has been introduced to take into account turbulence. Impli cit integration schemes with efficient numerical methods (CGS, GMRES a nd various preconditioning techniques) have also been implemented. Our interest is to present the whole method and to demonstrate its Limita tions on some well-known test cases in three-dimensional geometries. ( C) 1997 John Wiley & Sons, Ltd.