Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method

Scale-resolving simulations of turbulent flows in complex domains demand accurate and efficient numerical schemes, as well as geometrical flexibility. For underresolved situations, the avoidance of aliasing errors is a strong demand for stability. For continuous and discontinuous Galerkin schemes, an effective way to prevent aliasing errors is to increase the quadrature precision of the projection operator to account for the non-linearity of the operands (polynomial dealiasing, overintegration). But this increases the computational costs extensively. In this work, we present a novel spatially and temporally adaptive dealiasing strategy by projection filtering. We show this to be more efficient for underresolved turbulence than the classical overintegration strategy. For this novel approach, we discuss the implementation strategy and the indicator details, show its accuracy and efficiency for a decaying homogeneous isotropic turbulence and the transitional Taylor–Green vortex and compare it to the original overintegration approach and a state of the art variational multi-scale eddy viscosity formulation.