Optimized compact filtering schemes for computational aeroacoustics

摘要

Spurious waves are inevitably introduced in the simulation of computational aeroacoustics problems by finite difference schemes. Filters are proposed to damp the spurious waves as soon as they are generated. A family of filtering schemes, both interior and boundary, are optimized in this paper. The transfer functions of the filters are approximated to modified Gaussian functions and sharp spectral cutoffs are obtained. The advanced sequential quadratic programming method is employed to get the approximation. Although all of the optimized filters are stable and perform well in the computation, we find that the optimized fourth-order filters are sufficient for different kinds of requirements. The improvements of the accuracy and convenient application of the optimized filters are demonstrated when applied to one- and two-dimensional problems.