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Effect of Mesh Quality on Flux Reconstruction in Multi-dimensions

Published version
Peer-reviewed

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Authors

Watson, R 
Scillitoe, A 
Tucker, PG 

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.

Description

Keywords

Flux reconstruction, Fourier analysis, Von Neumann analysis, Mesh quality, Multiple dimensions

Journal Title

Journal of Scientific Computing

Conference Name

Journal ISSN

0885-7474
1573-7691

Volume Title

82

Publisher

Springer Science and Business Media LLC
Sponsorship
Engineering and Physical Sciences Research Council (EP/P020259/1)