An entropy-variable-based VMS/GLS method for the simulation of compressible flows on unstructured grids

The variational multiscale approach for large-eddy simulation is investigated within a finite element framework. A filtering analog of this method, providing a model, which shares basic structures with hyperviscosity models, is used and evaluated on a freely decaying isotropic turbulence in the limit of infinite Reynolds numbers. The method used is based on a symmetric form of the Navier–Stokes equations stabilized with a Galerkin/least-squares approach. The proposed procedure provides appealing results. It is as satisfactory as the use of Germano and Lilly’s dynamic algorithm, without stabilization flaws, and at a lower cost. Comparisons between numerical dissipation and the proper subgrid closure show that the variational multiscale models tend to compute a turbulent viscosity that accounts for the numerical sources of dissipation, which reveals an important feature for an intensive and robust use of VMS-large-eddy simulation.