Anisotropic adaptive stabilized finite element solver for RANS models

Summary Aerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge‐based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A variational multiscale‐stabilized finite element method is used to solve the incompressible Navier‐Stokes equations. Finally, the Spalart‐Allmaras turbulence model is solved using the streamline upwind Petrov‐Galerkin method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases. In this paper, we propose an adaptive anisotropic mesh methodology for performing accurate numerical simulations of turbulent flows past complex geometries. It couples a stabilized variational multiscale Navier‐Stokes modified solver to account for high stretched elements, a Spalart‐Allmaras turbulent model with a dynamic anisotropic mesh adaptation algorithm.