Simulation of the Compressible Taylor Green Vortex using High-Order Flux Reconstruction Schemes

In this paper, we investigate the ability of high-order Flux Reconstruction (FR) numerical schemes to perform accurate and stable computations of compressible turbulent flows on coarse meshes. Two new FR schemes, which are optimized for wave dissipation and dispersion properties, are compared to the nodal Discontinuous Galerkin and Spectral Difference methods recovered via the Energy-Stable FR method. The compressible Taylor-Green vortex benchmark problem at Re = 1600 is used as a simple a priori test of the numerics. Dissipation rates computed from kinetic energy, vorticity and pressure dilatation are plotted against reference solutions. Results show that at low mesh resolution the FR schemes are highly accurate across a range of orders of accuracy, although oscillations can appear in the solution at orders of six and above. While the FR method has a built-in stabilization mechanism, an additional means of damping these instabilities is required. The schemes vary in the amount of numerical dissipation and resolution of the turbulent spectrum. One of the optimized FR schemes (the OFR scheme) is shown to have greater spectral accuracy than any of the others tested, motivating its future usage for high-order, high-fidelity CFD.