Effect of Mesh Quality on Flux Reconstruction in Multi-dimensions

Theoretical methods are developed to understand the effect of non-uniform grids on Flux Reconstruction (FR) in multi-dimensions. A better theoretical understanding of the effect of wave angle and grid deformation is established. FR is shown to have a smaller variation in properties than some finite difference counterparts. Subsequent numerical experiments on the Taylor-Green Vortex with jittered elements show the effect of localised regions of expansion and contraction. The effect this had on Nodal DG-like schemes was to increase the dissipation, whereas for more typical FR schemes the effect was to increase the dispersion. Some comparison is made between second-order FR and a second-order finite volume (FV) scheme. FR is found to be more resilient to mesh deformation, however, FV is found to be more resolved when operated at second order on the same mesh.