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Optimised boundary compact finite difference schemes for computational aeroacoustics

By J.W. Kim

Abstract

A set of optimised boundary closure schemes is presented for use with compact central finite difference schemes in<br/>computational aeroacoustics (CAA) involving non-trivial boundaries. The boundary schemes are given in a form of<br/>non-central compact finite differences. They maintain fourth-order accuracy, a pentadiagonal matrix system and<br/>seven-point stencil which the main interior scheme employs. This paper introduces a new strategy to optimise the<br/>boundary schemes in the spectral domain and achieve the best resolution characteristics given a strict tolerance for<br/>the dispersion and dissipation errors. The boundary schemes are derived from sophisticated extrapolation of solutions<br/>outside the domain. The extrapolation functions are devised by combining polynomials and trigonometric series which<br/>contain extra control variables used to optimise the resolution characteristics. The differencing coefficients of the boundary<br/>schemes are determined in association with the existing coefficients of the interior scheme which is also optimised<br/>through an improved procedure in this paper. The accuracy of the proposed schemes is demonstrated by their application<br/>to CAA benchmark problems

Topics: QA, TL
Year: 2007
OAI identifier: oai:eprints.soton.ac.uk:47019
Provided by: e-Prints Soton
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