Abstract:

In this article spurious waves introduced in the computation of aeroacoustics are analyzed theoretically and filters are proposed to attenuate these waves as soon as they are generated. In order to obtain a sharp cutoff of the pentadiagonal filters, a modified Gaussian function is introduced. The transfer functions of the filters are forced to be approximated to the modified Gaussian function in a specific wavenumber domain. The sequential quadratic programming (SQP) method is employed to achieve the approximation. The accuracy, stability, and efficiency of computation are improved in the optimized filters, and they are more convenient for practical application. The improved performances of the optimized schemes are demonstrated through their application to one and two-dimensional problems.

Key words: compact scheme, filtering, finite difference method, sequential quadratic programming, computational aeroacoustics