Under-Resolved Simulation of Turbulent Flows Using a p-adaptive Discontinuous Galerkin Method

Abstract

In this work we present the main features of a p-adaptive Discontinuous Galerkin (DG) method, suited for the accurate and efficient simulation of turbulent flows. The method allows to locally adapt the polynomial degree of the solution within mesh elements (p-adaptation), obtaining significant reduction of the simulation time and memory, and, at the same time, preserving the high accuracy needed by Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES). Adaptation is driven by a simple error indicator, obtained blending two simple indicators based on the interface pressure jumps and on the decay of the coefficients of the modal expansion. Moreover, a load-balancing strategy is adopted during adaptation to achieve good parallel performances. Preliminary results are presented for the under-resolved simulation of the turbulent flows (i) around the NACA 0018 airfoil, \(Re_c = 100\,000\), \(M_\infty =0.2\) and angle of attack \(AoA = 10^\circ \), and (ii) around a rounded leading-edge flat plate (the T3L test case of the ERCOFTAC suite).