Optimised boundary compact finite difference schemes for computational aeroacoustics

Kim, J.W. (2007) Optimised boundary compact finite difference schemes for computational aeroacoustics. Journal of Computational Physics, 225 (1), 995-1019. (doi:10.1016/j.jcp.2007.01.008).

Record type: Article

Abstract

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