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Adaptive variational multiscale finite element method for high Reynolds number flows

by Professor Elie Hachem, Computing and Fluids Research Group, MINES ParisTech, PSL – Research University, CEMEF – Centre for material forming, CNRS UMR 7635, Sophia-Antipolis.

Abstract:

In this work, we propose to show that adaptive anisotropic meshing based on a posteriori estimation can be addressed for incompressible Navier-Stokes equations at high Reynolds number. First, a simple edge based error estimator is presented for detecting sharp gradients, inner and boundary layers under the constraint of a fixed number of elements, thus controlling the computational cost. Then a Variational MultiScale (VMS) stabilized finite element method is employed to solve the incompressible Navier-Stokes equations. The basic idea is to consider that the unknowns can be split in two components, coarse and fine, corresponding to different scales or levels of resolution. By solving first the fine scales and then replacing their effect into the large scales, we obtain a new system that acts as an implicit Large Eddy Simulation (ILES). However, it requires tuning of the stabilization coefficients in both the convective and diffusive terms to take into account highly stretched elements with an anisotropic ratio of the order of O(1 : 1000). Finally, the interested part of this talk, we want to verify how accurate may become combining anisotropic unsteady mesh adaptation with the ILES method and how the solution behaves in particular near the boundary layers when compared to DNS results. Therefore, several test cases, 3D industrial studies and confrontation with literature are proposed.