Abstract
Theoretical methods are developed to understand the effect of nonuniform 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.
Original language | English |
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Article number | 77 |
Number of pages | 36 |
Journal | Journal of Scientific Computing |
Volume | 82 |
DOIs | |
Publication status | Published - 12 Mar 2020 |