Inviscid and Viscous Simulations of the Taylor-Green Vortex Flow Using a Modal Discontinuous Galerkin Approach

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

“…32 and is the subject of ongoing investigation. Nevertheless, 5 predicted by the FR schemes was found to converge to the correct solution with grid refinement, as was also observed by Chapelier et al [5]. Figure 9 (a -f) displays energy spectra of the p 3 (a, b), p 4 (c, d) and p 5 (e, f) FR-nDG, FR-SD and OFR solutions on the coarse and medium meshes at time t = 9 seconds compared to the reference solution computed using a pseudo-spectral method on a 512 3 mesh by Carton de Wiart et al [37].…”

“…The TGV was one of the problems in the 1st, 2nd and 3rd International Workshops on High-Order CFD Methods [38][39][40]) and is considered to be a challenging test for high-order methods. Various authors have used high-order discontinuous methods on the TGV test case with excellent results, including classical DG [5,36,37], DGSEM [9,29] and a preliminary study by Bull and Jameson using the FR-SD scheme [41]. Wang gives a review of the current status of high-order methods for several problems including the TGV [1].…”

“…The dissipation rate due to pressure dilatation, 5 , measures the effect of compressibility on the dissipation of turbulent energy. Figure 8 plots 5 for the FR-nDG, FR-SD and OFR schemes at p 4 on the medium mesh versus the DRP scheme on the 64 3 and 512 3 meshes.…”

“…Over the past two decades, Discontinuous Galerkin (DG) methods have proved to be highly successful for high-order accurate simulations in complex geometry owing to their formulation on full hybrid meshes [3,4]. Classical DG methods construct integral operators over element volumes and surfaces by integrating the equations by parts and represent the solution within each element as a modal expansion of locally orthogonal polynomials [5]. This has the advantages of making the mass matrix diagonal and enabling exact evaluation of the integrals, but classical DG can be expensive if standard…”

“…Gassner [9], Diosady and Murman [29], Chapelier et al [5], Don et al [35], Johnsen et al [36] and Carton de Wiart et al [37]. The TGV was identified as a challenging problem for high-order methods in the 1st, 2nd and 3rd International Workshops on High-Order CFD Methods [38][39][40].…”