Optimised boundary compact finite difference schemes for computational aeroacoustics

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.