An implicit mixed finite-volume-finite-element method for solving 3D turbulent compressible flows

Abstract

The development of new aeronautic projects require accurate and efficient simulations of compressible flows in complex geometries. It is well 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 and 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 extended 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 element method, while the other terms are computed with a finite volume method. Finite volume cells are built around each node by means of the medians. The convective fluxes are evaluated with the approximate Riemann solver of Roe coupled with the van Albada limiter. The standard κ-e model has been introduced to take into account turbulence. Implicit integration schemes with efficient numerical methods (CGS, GMRES and various preconditioning techniques) have also been implemented