Numerical Investigation of the Inviscid Taylor-Green Vortex Using an Adaptive Filtering Method for a Modal Discontinuous Galerkin Method

Abstract

Implicit Large Eddy Simulation and under-resolved Direct Numerical Simulation bypass the complexity and uncertainty of turbulence modelling by using the numerical dissipation of the scheme as a subgrid scale model. High-order methods allow for more accurate capturing of smaller scale structures but suffer from energy pile-up in the higher modes which leads to instability in under-resolved applications. This work presents a filtered modal Discontinuous Galerkin method which adaptively determines the filter strength, avoiding unnecessary degradation of accuracy while maintaining stability. The method is applied to the inviscid Taylor-Green Vortex, a challenging test case which exhibits under-resolved turbulence for which few published results exist. This goal of this work is to present the adaptive filtering method which achieves robustness and accuracy despite a low number of degrees of freedom, as well as to publish a quantity of relevant data for the inviscid TGV problem.