Two different and recent CFD activities of ONERA are presented.
First, an extension of the classical implicit stages for the numerical simulation of compressible turbulent flows with backward-Euler schemes is described. When using a large stencil viscous flux discretization (when this flux is computed from cell-centred evaluation of velocity and temperature gradients), a 5-point per mesh direction approximate linearization of the viscous flux balance is proposed. The space discretization and implicit stages are described. Results of a scalar linear stability analysis are presented. Multigrid and monogrid computations of turbulent flow around two external configurations are performed with Wilcox�s �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, lead to the best convergence rates.
Then, a contribution to discrete direct differentiation method and discrete adjoint vector method for the differentiation of aerodynamic functions with respect to design parameters is described. When dealing with turbulent flows, the differentiation of the viscous flux of (RANS) equations is discussed. Some authors use the assumption of Constant Turbulent Eddy Viscosity [CTEV] whereas other differentiate accurately the (RANS) equations and the turbulence model. The accurate differentiation of Michel et al.�s turbulence model is presented. A study of gradient accuracy for 3D ONERA wing has been carried out. Results point out the benefit of the accurate linearization.
