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A wavelet‐based variational multiscale method for the LES of incompressible flows in a high‐order DG‐FEM framework

This work focuses upon the development of a wavelet‐based variant of the variational multiscale method (VMS) for accurate and efficient large eddy simulation (LES) called wavelet‐based VMS‐LES (WMS‐LES). This approach has been incorporated within the framework of a high‐order incompressible flow solver based upon the pressure‐stabilized discontinuous Galerkin finite element method (DG‐FEM). The VMS approach is designed to produce an a priori scale separation of the governing equations, in a manner which makes no assumptions on either the boundary conditions or the mesh uniformity. Using second‐generation wavelets (SGWs) elementwise for scale separation ensures, on one hand, the preservation of the computational compactness of the DG‐FEM scheme and, on the other hand, the ability to achieve scale separation in wavenumber space. The optimal space‐frequency localization property of the SGW provides an improvement over the commonly used Legendre polynomials. The suitability of the elementwise SGW scale‐separation operation as a tool for error indication has been demonstrated in an h‐adaptive computation of the reentrant corner test case. Finally, the DG‐FEM solver and the WMS‐LES method have been assessed through simulations upon the three‐dimensional Taylor‐Green vortex test case. Our results indicate that the WMS‐LES approach exhibits a distinct improvement over the monolevel LES approach. This effect is not produced by a change in the magnitude of the subgrid dissipation but rather by the redistribution of the subgrid dissipation in wavenumber space.