Large stencil viscous flux linearization for the simulation of 3D compressible turbulent flows with backward-Euler schemes

The purpose of this article is to study different approximate linearizations of the RANS equations viscous fluxes, for numerical simulations of compressible turbulent flows with backward-Euler schemes. The explicit convective flux under consideration is centred with artificial dissipation. The discrete viscous flux, calculated from cell-centred evaluation of the gradients, needs less computations and memory storage than other discretizations. But, in other respects, the balance of this numerical flux has a large stencil, which is not coherent with the 3-point per mesh direction stencil of classical implicit stages. Therefore 3-point and 5-point per mesh direction approximate linearizations are built from the thin layer flux formula. The stability condition of the corresponding backward-Euler schemes is given for a scalar linear equation (for the basic non-factored version of scheme and with LU-relaxation). Multigrid and monogrid computations of turbulent flow around two external configurations are performed with Wilcox’s k–ω turbulence model. The 5-point per mesh direction linearizations, coherent with the differential of the fluxes balance of thin layer approximation of explicit viscous fluxes, leads to the most efficient implicit stages.