Abstract
Theoretical methods are developed to understand the effect of non-uniform
grids on Flux Reconstruction (FR) in multi-dimensions. The analysis reveals
that the same effect of expanding and contracting grids is seen in two
dimensions as in one dimension. Namely, that expansions cause instability and
contractions cause excess dissipation. Subsequent numerical experiments on the
Taylor-Green Vortex with jittered elements show the effect of localised regions
of expansion and contraction, with an initial increase in the kinetic energy
observed on non-uniform meshes. Some comparison is made between second-order FR
and second-order finite volume (FV). 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. In both cases, it is recommended that a kinetic energy
preserving/conservation formulation should be used as this can greatly increase
resilience to mesh deformation.