ACCURATE FINITE-DIFFERENCE METHODS FOR TIME-HARMONIC WAVE-PROPAGATION

Finite difference methods for solving problems of time-harmonic acoust ics are developed and analyzed. Multi-dimensional inhomogeneous proble ms with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted- average representation is less sensitive to transition in wave resolut ion (due to variable wave numbers or non-uniform grids) than the stand ard pointwise representation. Further enhancement in method performanc e is obtained by basing the stencils on generalizations of Padi! appro ximation, or generalized definitions of the derivative, reducing spuri ous dispersion, anisotropy, and reflection, and by improving the repre sentation of source terms. The resulting schemes have fourth-order acc urate local truncation error on uniform grids and third order in the n onuniform case. Guidelines for discretization pertaining to grid orien tation and resolution are presented. (C) 1995 Academic Press, Inc.