Improving the boundary efficiency of a compact finite difference scheme through optimising its composite template
Improving the boundary efficiency of a compact finite difference scheme through optimising its composite template
This paper presents efforts to improve the boundary efficiency and accuracy of a compact finite difference scheme, based on its composite template. Unlike precursory attempts the current methodology is unique in its quantification of dispersion and dissipation errors, which are only evaluated after the matrix system of equations has been rearranged for the derivative. This results in a more accurate prediction of the boundary performance, since the analysis is directly based on how the derivative is represented in simulations. A genetic algorithm acts as a comprehensive method for the optimisation of the boundary coefficients, incorporating an eigenvalue constraint for the linear stability of the matrix system of equations. The performance of the optimised composite template is tested on one-dimensional linear wave convection and two-dimensional inviscid vortex convection problems, with uniform and curvilinear grids. In all cases, it yields substantial accuracy and efficiency improvements while maintaining stable solutions and fourth-order accuracy.
9-25
Turner, J.
8618df92-3b0c-46e6-a482-dd12b261d9a7
Haeri, S.
8e2f9ded-d4c7-4ae3-9fdb-db91f5f9ba9e
Kim, J.W.
fedabfc6-312c-40fd-b0c1-7b4a3ca80987
15 October 2016
Turner, J.
8618df92-3b0c-46e6-a482-dd12b261d9a7
Haeri, S.
8e2f9ded-d4c7-4ae3-9fdb-db91f5f9ba9e
Kim, J.W.
fedabfc6-312c-40fd-b0c1-7b4a3ca80987
Turner, J., Haeri, S. and Kim, J.W.
(2016)
Improving the boundary efficiency of a compact finite difference scheme through optimising its composite template.
Computers & Fluids, 138, .
(doi:10.1016/j.compfluid.2016.08.007).
Abstract
This paper presents efforts to improve the boundary efficiency and accuracy of a compact finite difference scheme, based on its composite template. Unlike precursory attempts the current methodology is unique in its quantification of dispersion and dissipation errors, which are only evaluated after the matrix system of equations has been rearranged for the derivative. This results in a more accurate prediction of the boundary performance, since the analysis is directly based on how the derivative is represented in simulations. A genetic algorithm acts as a comprehensive method for the optimisation of the boundary coefficients, incorporating an eigenvalue constraint for the linear stability of the matrix system of equations. The performance of the optimised composite template is tested on one-dimensional linear wave convection and two-dimensional inviscid vortex convection problems, with uniform and curvilinear grids. In all cases, it yields substantial accuracy and efficiency improvements while maintaining stable solutions and fourth-order accuracy.
Text
CAF2016-Turner-Accepted.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 12 August 2016
e-pub ahead of print date: 13 August 2016
Published date: 15 October 2016
Organisations:
Aerodynamics & Flight Mechanics Group
Identifiers
Local EPrints ID: 399504
URI: http://eprints.soton.ac.uk/id/eprint/399504
ISSN: 0045-7930
PURE UUID: 146997d9-5482-4f9f-975b-5920dc0e6e51
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Date deposited: 18 Aug 2016 12:17
Last modified: 15 Mar 2024 05:49
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Author:
J. Turner
Author:
S. Haeri
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