Inviscid and Viscous Simulations of the Taylor-Green Vortex Flow Using a Modal Discontinuous Galerkin Approach

A modal Discontinuous Galerkin (DG) method is assessed for the Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of freely decaying turbulence. We consider as benchmark test case the TaylorGreen vortex flow. Inviscid computations show the conservation and dissipation properties of the DG scheme in the context of 3D non-linear flow problems. DG DNS computations carried at low and moderate Reynolds numbers (Re = 400 and Re = 1600, respectively) show good agreement with a reference solution generated using a Fourier pseudo-spectral code. LES computations are carried out at larger Reynolds number (Re = 3000), and compared to a reference filtered DNS. The Variational Multiscale Simulation framework, which can be straightforwardly implemented in a modal DG code is compared to the classical Smagorinsky approach for LES.

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