Dispersion and Diffusion analysis of discontinuous spectral element methods for LES
Nektar++ has been recently used to assess theoretical estimates of the dispersion and diffusion properties of discontinuous spectral element methods, in particular, discontinuous Galerkin (Mengaldo et al., Computers & Fluids 2017) and flux reconstruction schemes (Mengaldo et al. Journal of Computational Physics 2018).
Figure 1. Simulations of grid turbulence in the limit of vanishing viscosity (very high Reynolds number) for 2 different Riemann solvers and 2 Mach numbers. The Rusanov (also known as local Lax Friedrichs flux) shows poorer performance than the more physically-faithful Roe flux).
Both studies enriched the understanding of the behavior of these methods for under-resolved simulations that are of interest primarily (but not limited) to the aerospace and automotive industry (e.g. high-Reynolds number applications). The study fits within the framework of high-resolution implicit large-eddy simulations that is being pushed forward by several research centers and practitioners and considers non-periodic flows via the spatial eigensolution analysis framework proposed in (Mengaldo et al., Computers & Fluids 2017). The latter aspect expands the dispersion/diffusion analysis envelope that is traditionally used, that is considering periodic problems only, thus providing an effective tool for constructing high-fidelity simulation tools of general problems not subject to the period boundary conditions.