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

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Title: An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements
Author(s): Witherden, FD
Park, JS
Vincent, PE
Item 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.
Publication Date: 21-Apr-2016
Date of Acceptance: 4-Apr-2016
URI: http://hdl.handle.net/10044/1/33872
DOI: http://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.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K503381/1
EP/L000407/1
EP/K027379/1
EP/M50676X/1
Keywords: 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
Open Access location: http://download.springer.com/static/pdf/315/art%253A10.1007%252Fs10915-016-0204-y.pdf?originUrl=http://link.springer.com/article/10.1007/s10915-016-0204-y&token2=exp=1466511116~acl=/static/pdf/315/art%25253A10.1007%25252Fs10915-016-0204-y.pdf?originUrl=http%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs10915-016-0204-y*~hmac=445bc435a8146784ebb824a0e82b47aa98dc102c1dc4cb52c501622c2f018c8f
Appears in Collections:Faculty of Engineering
Aeronautics



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