Evaluation of the spectral element dynamic model for LES on unstructured, deformed meshes

Abstract

Discontinuous finite element methods (DFEM) such as the discontinuous Galerkin (DG) (Cockburn et al, Discontinuous Galerkin methods: Theory, computation, and applications. Springer, Berlin, 2000), [1] or the spectral difference (SD) (Kopriva and Kolias, J Comput Phys 125(1):244–261, 1996), [7], (Liu et al, J Comput Phys 216(2):780–801, 2006), [9], (Wang et al, J Sci Comput 32(1):45–71, 2007), [21] methods show a strong potential for the direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent flows on realistic geometries. These methods are characterized by a rather peculiar mix of features, such as their high-orders of accuracy, the ability to handle unstructured meshes, curved boundary elements and the compactness of the stencil, which allows for optimal parallelism. The extremely low level of numerical dissipation which can be achieved when high-orders are selected, and the consequent significant increase in resolving power, make DFEM particularly well suited for LES.