An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements

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Author(s)

Witherden, FD

Park, JS

Vincent, PE

Type

Journal Article

Abstract

The flux reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution point placement on the stability and accuracy of FR schemes on tetrahedral grids. To accomplish this we generate a large number of solution point candidates that satisfy various criteria at polynomial orders ℘=3,4,5℘=3,4,5 . We then proceed to assess their properties by using them to solve the non-linear Euler equations on both structured and unstructured meshes. The results demonstrate that the location of the solution points is important in terms of both the stability and accuracy. Across a range of cases it is possible to outperform the solution points of Shunn and Ham for specific problems. However, there appears to be a degree of problem-dependence with regards to the optimal point set, and hence overall it is concluded that the Shunn and Ham points offer a good compromise in terms of practical utility.

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Date Issued

2016-04-21

Date Acceptance

2016-04-04

Citation

Journal of Scientific Computing, 2016, 69 (2), pp.905-920

URI

http://hdl.handle.net/10044/1/33872

DOI

https://www.dx.doi.org/10.1007/s10915-016-0204-y

ISSN

0885-7474

Publisher

Springer Verlag

Start Page

905

End Page

920

Journal / Book Title

Journal of Scientific Computing

Volume

69

Issue

2

Copyright Statement

© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

License URL

http://creativecommons.org/licenses/by/4.0/

Sponsor

Engineering & Physical Science Research Council (EPSRC)

Engineering & Physical Science Research Council (E

Engineering & Physical Science Research Council (EPSRC)

Engineering & Physical Science Research Council (EPSRC)

Grant Number

EP/K503381/1

EP/L000407/1

EP/K027379/1

EP/M50676X/1

Subjects

Science & Technology

Physical Sciences

Mathematics, Applied

Mathematics

Flux reconstruction

High-order methods

Discontinuous galerkin

SYMMETRIC QUADRATURE-RULES

Applied Mathematics

Numerical And Computational Mathematics

Computation Theory And Mathematics

Publication Status

Published