Assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number

• Published in: International journal for numerical methods in fluids Vol. 74; no. 7; pp. 469 - 493
• Main Authors: Carton de Wiart, C., Hillewaert, K., Duponcheel, M., Winckelmans, G.
• Format: Journal Article Web Resource
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 10.03.2014; Wiley Subscription Services, Inc; John Wiley & Sons
• Subjects: Aerospace & aeronautics engineering; Computational fluid dynamics; Computer science; direct numerical simulation; discontinuous Galerkin method; Dissipation; Engineering, computing & technology; Errors; Finite element method; Fluid flow; Galerkin methods; High Reynolds number; Ingénierie aérospatiale; Ingénierie mécanique; Ingénierie, informatique & technologie; Mathematical models; Mechanical engineering; Sciences informatiques; Taylor-Green vortex; unstructured meshes
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.3859

SUMMARYThis paper focuses on the assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number. The Taylor–Green vortex at Re = 1600 is considered. The results are compared with those obtained using a pseudo‐spectral solver, converged on a 5123 grid and taken as the reference. The temporal evolution of the dissipation rate, visualisations of the vortical structures and the kinetic energy spectrum at the instant of maximal dissipation are compared to assess the results. At an effective resolution of 2883, the fourth‐order accurate discontinuous Galerkin method (DGM) solution (p = 3) is already very close to the pseudo‐spectral reference; the error on the dissipation rate is then essentially less than a percent, and the vorticity contours at times around the dissipation peak overlap everywhere. At a resolution of 3843, the solutions are indistinguishable. Then, an order convergence study is performed on the slightly under‐resolved grid (resolution of 1923). From the fourth order, the decrease of the error is no longer significant when going to a higher order. The fourth‐order DGM is also compared with an energy conserving fourth‐order finite difference method (FD4). The results show that, for the same number of DOF and the same order of accuracy, the errors of the DGM computation are significantly smaller. In particular, it takes 7683 DOF to converge the FD4 solution. Finally, the method is also successfully applied on unstructured high quality meshes. It is found that the dissipation rate captured is not significantly impacted by the element type. However, the element type impacts the energy spectrum in the large wavenumber range and thus the small vortical structures. In particular, at the same resolution, the results obtained using a tetrahedral mesh are much noisier than those obtained using a hexahedral mesh. Those obtained using a prismatic mesh are already much better, yet still slightly noisier. Copyright © 2013 John Wiley & Sons, Ltd. The Taylor–Green vortex at Re = 1600 is considered to assess a discontinuous Galerkin method for the direct numerical simulation of high Reynolds number flows. Grid convergence, order convergence and comparison with the fourth‐order finite difference method are performed on hexahedral grids, showing the ability of discontinuous Galerkin method to capture the flow features using reasonably small resolution. Finally, the method is successfully applied on unstructured meshes composed of prismatic or tetrahedral elements. Although the energy spectrum is overpredicted on the high wavenumber range, the dissipation rate captured is not significantly impacted by the element type.