Towards a genuinely stable boundary closure for pentadiagonal compact finite difference schemes
Towards a genuinely stable boundary closure for pentadiagonal compact finite difference schemes
A new optimisation strategy to develop high-order and genuinely stable boundary closure schemes for a pentadiagonal, seven-point stencil, compact finite difference system is proposed. Previous approaches to developing boundary compact schemes often yielded either potential instabilities or non-optimal accuracy in the numerical solutions. In the present optimisation, the numerical accuracy and stability of the compact differencing system are addressed simultaneously by maximising the global accuracy of the system under stability constraints that are enhanced by a non-Dirichlet boundary condition. A unified extrapolation method is proposed to assist in the derivation of boundary schemes. A set of optimised boundary compact schemes is obtained for use along with an existing interior compact scheme. The resultant fourth-order compact finite difference system is applied to flow and acoustic benchmark problems as well as a large-eddy simulation, demonstrating superior performance in numerical stability, accuracy, and spatial resolution.
Boundary closure, Compact schemes, High-order finite difference, Numerical stability, Optimisation
Wu, Long
9787473b-a81a-47ce-a696-22afa8c2204b
Kim, Jae Wook
fedabfc6-312c-40fd-b0c1-7b4a3ca80987
1 May 2024
Wu, Long
9787473b-a81a-47ce-a696-22afa8c2204b
Kim, Jae Wook
fedabfc6-312c-40fd-b0c1-7b4a3ca80987
Wu, Long and Kim, Jae Wook
(2024)
Towards a genuinely stable boundary closure for pentadiagonal compact finite difference schemes.
Journal of Computational Physics, 504, [112887].
(doi:10.1016/j.jcp.2024.112887).
Abstract
A new optimisation strategy to develop high-order and genuinely stable boundary closure schemes for a pentadiagonal, seven-point stencil, compact finite difference system is proposed. Previous approaches to developing boundary compact schemes often yielded either potential instabilities or non-optimal accuracy in the numerical solutions. In the present optimisation, the numerical accuracy and stability of the compact differencing system are addressed simultaneously by maximising the global accuracy of the system under stability constraints that are enhanced by a non-Dirichlet boundary condition. A unified extrapolation method is proposed to assist in the derivation of boundary schemes. A set of optimised boundary compact schemes is obtained for use along with an existing interior compact scheme. The resultant fourth-order compact finite difference system is applied to flow and acoustic benchmark problems as well as a large-eddy simulation, demonstrating superior performance in numerical stability, accuracy, and spatial resolution.
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More information
Accepted/In Press date: 24 February 2024
e-pub ahead of print date: 28 February 2024
Published date: 1 May 2024
Additional Information:
Funding information:
The authors thank EPSRC (Engineering and Physical Sciences Research Council) for the computational time made available on the UK supercomputing facility ARCHER2 via the UK Turbulence Consortium (EP/R029326/1). The authors also acknowledge the use of IRIDIS-5 high-performance computing facility and associated support services at the University of Southampton.
Publisher Copyright:
© 2024 The Author(s)
Keywords:
Boundary closure, Compact schemes, High-order finite difference, Numerical stability, Optimisation
Identifiers
Local EPrints ID: 487623
URI: http://eprints.soton.ac.uk/id/eprint/487623
ISSN: 0021-9991
PURE UUID: d09f1816-49c1-4675-b955-68d2d84d2bc4
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Date deposited: 29 Feb 2024 17:39
Last modified: 27 Apr 2024 02:06
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Author:
Long Wu
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