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Optimized compact finite difference schemes with maximum resolution

Optimized compact finite difference schemes with maximum resolution
Optimized compact finite difference schemes with maximum resolution
Direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high-resolution characteristics in the evaluation of spatial derivatives. Compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders. An analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes, based on the idea of the minimization of dispersive (phase) errors in the wave number domain, and these are applied to the analytic optimization of multidiagonal compact schemes. Actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections, and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases, respectively. From these comparisons, the usefulness of an optimized high-order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed. For the optimized high-order spatial schemes, the feasibility of using classical high-order Runge-Kutta time advancing methods is investigated.
0001-1452
887-893
Kim, J.W.
fedabfc6-312c-40fd-b0c1-7b4a3ca80987
Lee, D.J.
07e9aeba-8cdd-4476-bd03-b936bc2ca8c1
Kim, J.W.
fedabfc6-312c-40fd-b0c1-7b4a3ca80987
Lee, D.J.
07e9aeba-8cdd-4476-bd03-b936bc2ca8c1

Kim, J.W. and Lee, D.J. (1996) Optimized compact finite difference schemes with maximum resolution. AIAA Journal, 34 (5), 887-893.

Record type: Article

Abstract

Direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high-resolution characteristics in the evaluation of spatial derivatives. Compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders. An analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes, based on the idea of the minimization of dispersive (phase) errors in the wave number domain, and these are applied to the analytic optimization of multidiagonal compact schemes. Actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections, and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases, respectively. From these comparisons, the usefulness of an optimized high-order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed. For the optimized high-order spatial schemes, the feasibility of using classical high-order Runge-Kutta time advancing methods is investigated.

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Published date: 1996
Organisations: Aerodynamics & Flight Mechanics

Identifiers

Local EPrints ID: 23038
URI: http://eprints.soton.ac.uk/id/eprint/23038
ISSN: 0001-1452
PURE UUID: 6a213b9b-cb8c-4e32-a363-fa3250e3106c
ORCID for J.W. Kim: ORCID iD orcid.org/0000-0003-0476-2574

Catalogue record

Date deposited: 31 Jan 2007
Last modified: 16 Mar 2024 03:42

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Contributors

Author: J.W. Kim ORCID iD
Author: D.J. Lee

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