Assessing standard and kinetic energy conserving volume fluxes in discontinuous Galerkin formulations for marginally resolved Navier-Stokes flows. (15th June 2020)

• Record Type: Journal Article
• Authors: Klose, Bjoern F.; Jacobs, Gustaaf B.; Kopriva, David A.
• Is Part Of: Computers & fluids. Volume 205(2020)
• Publication Date: 2020-06-15
• Subjects: Discontinuous Galerkin -- Kinetic energy conservation -- Navier-Stokes -- Airfoil; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2020.104557
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Assessment of kinetic energy conserving volume fluxes in marginally resolved flows. The standard Gauss DG scheme is more accurate than Gauss-Lobatto variants. The split-form Gauss-Lobatto scheme is numerically robust when under-resolving. Examples of Taylor-Green vortex, planar jet, circular cylinder and cambered irfoil. 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.