Assessing Standard and Kinetic Energy Conserving Discontinuous Galerkin Formulations for Marginally Resolved Navier-Stokes Flows

TL;DR

This paper compares standard and kinetic energy conserving discontinuous Galerkin methods for simulating complex, under-resolved Navier-Stokes flows, highlighting robustness and accuracy differences in practical engineering scenarios.

Contribution

It demonstrates that the kinetic energy conserving formulation offers superior robustness over the standard scheme in marginally resolved flow simulations.

Findings

Kinetic energy conserving scheme is more robust for under-resolved flows.

Standard scheme achieves higher accuracy with Gauss quadrature.

Split form shows lower numerical robustness and spurious oscillations.

Abstract

The robustness and accuracy of marginally resolved discontinuous Galerkin spectral element computations are evaluated for the standard formulation and a kinetic energy conserving split form on complex flow problems of physical and engineering interest, including the flow over a square cylinder, an airfoil and a plane jet. It is shown that the kinetic energy conserving formulation is significantly more robust than the standard scheme for under-resolved simulations. A disadvantage of the split form is the restriction to Gauss-Lobatto nodes with the inherent underintegration and lower accuracy as compared to Gauss quadrature used with the standard scheme. While the results support the higher accuracy of the standard Gauss form, lower numerical robustness and spurious oscillations are evident in some cases, giving the advantage to the kinetic energy conserving scheme for marginally resolved numerical simulations.