Effect of Mesh Quality on Flux Reconstruction in Multi-Dimensions

Will Trojak; Rob Watson; Ashley Scillitoe; Paul G. Tucker

doi:10.1007/s10915-020-01184-2

Effect of Mesh Quality on Flux Reconstruction in Multi-Dimensions

Will Trojak^*, Rob Watson, Ashley Scillitoe, Paul G. Tucker

^*Corresponding author for this work

School of Mechanical and Aerospace Engineering

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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
Article number	77
Number of pages	36
Journal	Journal of Scientific Computing
Volume	82
DOIs	https://doi.org/10.1007/s10915-020-01184-2
Publication status	Published - 12 Mar 2020

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Effect of Mesh Quality on Flux Reconstruction in Multi-dimensions
© 2020 The Authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
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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.",

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