Numerically robust 3-D finite element Reynolds Averaged Navier-Stokes solver for the study of turbulent supersonic external flows

Abstract A 3-D finite element Reynolds Averaged Navier-Stokes solver for supersonic flows is presented and described. The solver has been developed to target industrial aerodynamics applications in the field of reusable launcher design and, therefore, specific emphasis has been put on maximizing numerical robustness. To achieve this goal, the turbulence model can be chosen beforehand between two options: a k -e formulation or a combined algebraic/ k -e scheme that gets the best characteristics out of both formulations. In addition, to ensure quick convergence in the early stages of the time-marching procedure, a theoretical analysis is performed to gather and implement into the algorithm the limiting behavior of k and e wherever turbulent production is dominant. Results of the validation campaign are presented, a practical application case is shown, and finally, conclusions are drawn.