The University of Southampton
University of Southampton Institutional Repository

A priori grid quality estimation for high-order finite differencing

A priori grid quality estimation for high-order finite differencing
A priori grid quality estimation for high-order finite differencing
Structured grids using the finite differencing method contain two sources of grid-induced truncation errors. The first is dependent on the solution field. The second is related only to the metrics of the grid transformation. The accuracy of the grid transformation metrics is affected by the inverse metrics, which are spatial derivatives of the grid in the generalised coordinates. The truncation errors contained in the inverse metrics are generated by the spatial schemes. Fourier analysis shows that the dispersion errors, by spatial schemes, have similarities to the transfer function of spatial filters. This similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid-induced errors. An inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy, for three common geometric features found in grids: abrupt changes in the grid metrics, skewness, and grid stretching. A strong correlation is obtained, provided that the grid transformation errors are the most significant sources of error.
0021-9991
629-643
Fattah, Ryu
658d0694-d683-4839-89a0-b95601ebe365
Angland, David
b86880c6-31fa-452b-ada8-4bbd83cda47f
Zhang, Xin
3056a795-80f7-4bbd-9c75-ecbc93085421
Fattah, Ryu
658d0694-d683-4839-89a0-b95601ebe365
Angland, David
b86880c6-31fa-452b-ada8-4bbd83cda47f
Zhang, Xin
3056a795-80f7-4bbd-9c75-ecbc93085421

Fattah, Ryu, Angland, David and Zhang, Xin (2016) A priori grid quality estimation for high-order finite differencing. Journal of Computational Physics, 315, 629-643. (doi:10.1016/j.jcp.2016.03.063).

Record type: Article

Abstract

Structured grids using the finite differencing method contain two sources of grid-induced truncation errors. The first is dependent on the solution field. The second is related only to the metrics of the grid transformation. The accuracy of the grid transformation metrics is affected by the inverse metrics, which are spatial derivatives of the grid in the generalised coordinates. The truncation errors contained in the inverse metrics are generated by the spatial schemes. Fourier analysis shows that the dispersion errors, by spatial schemes, have similarities to the transfer function of spatial filters. This similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid-induced errors. An inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy, for three common geometric features found in grids: abrupt changes in the grid metrics, skewness, and grid stretching. A strong correlation is obtained, provided that the grid transformation errors are the most significant sources of error.

Text
A priori grid quality estimation for high order nite.pdf - Accepted Manuscript
Download (5MB)

More information

Accepted/In Press date: 29 March 2016
e-pub ahead of print date: 4 April 2016
Published date: 15 June 2016
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 394021
URI: http://eprints.soton.ac.uk/id/eprint/394021
ISSN: 0021-9991
PURE UUID: 7a6de6a6-a730-4a06-9da9-9074c0d0fc61

Catalogue record

Date deposited: 10 May 2016 11:19
Last modified: 15 Mar 2024 05:33

Export record

Altmetrics

Contributors

Author: Ryu Fattah
Author: David Angland
Author: Xin Zhang

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×