| Computational Aeroacoustics (CAA) combines the disciplines from both aeroacoustics and computational fluid dynamics and deals with the sound generation and propagation in association with the dynamics of the fluid flow, and its interaction with the geometry of the surrounding structures. To conduct such computations, it is essential that the numerical techniques for acoustic problems contain low dissipation and dispersion error for a wide range of length and time scales, can satisfy the nonlinear conservation laws, and are capable of dealing with geometric variations.; In this dissertation, we first investigate two promising numerical methods for treating convective transport: the dispersion-relation-preservation (DRP) scheme, proposed by Tam and Webb, and the space-time a-epsilon method, developed by Chang. Between them, it seems that for long waves, errors grow slower with the space-time a-epsilon scheme, while for short waves, often critical for acoustics computations, errors accumulate slower with the DRP scheme. Based on these findings, two optimized numerical schemes, the dispersion-relation-preserving (DRP) scheme and the optimized prefactored compact (OPC) scheme, originally developed using the finite difference approach, are recast into the finite volume form so that nonlinear physics can be better handled. Finally, the Cartesian grid, cut-cell method is combined with the high-order finite-volume schemes to offer additional capabilities of handling complex geometry. The resulting approach is assessed against several well identified test problems, demonstrating that it can offer accurate and effective treatment to some important and challenging aspects of acoustic problems. |
