| High order finite difference schemes are generally less dispersive, less dissipative and more isotropic than low order schemes. They are, therefore, better suited for the solution of wave propagation problems. High order schemes, however, support spurious numerical waves which have no relationship to the waves of the original partial differential equations. The large stencils associated with the high order schemes also make the implementation of boundary conditions more difficult. A number of fundamental difficulties which occur when high order finite difference schemes are used to solve computational aeroacoustics and flow problems are investigated and resolved. The research work includes: (a) Development of an artificial selective damping technique for the elimination of spurious numerical waves; (b) Formation of a set of solid wall boundary conditions for high order finite difference schemes; (c) Design of a family of multi-domain multiple-time-step high order finite difference algorithms for the solution of acoustics and flow problems with large disparate length scales. A sequence of direct numerical simulations are performed to demonstrate the effectiveness of all the proposed methods. |
