NONREFLECTING BOUNDARY-CONDITIONS BASED ON KIRCHHOFF-TYPE FORMULAS

Exact nonreflecting boundary conditions are considered for exterior three-dimensional lime-dependent wave problems. These include a nonlocal condition for acoustic waves based on Kirchhoff's formula, orginally proposed by L. Ting and M. J. Miksis (J. Acoust. Sec. Am. 80, 1825 (1986), and an analogous condition for elastic waves. These conditions are computationally attractive in that their temporal nonlocality is limited to a fixed amount of past information. However, when a standard nondissipative finite difference stencil is used as the interior scheme, a long-time instability is exhibited in the numerical solution. This instability is analyzed for a simple one-dimensional model problem. It is eliminated once the standard interior scheme is replaced by the dissipative Lax-Wendroff scheme. In this case stability is demonstrated experimentally, and it is also established theoretically in the one-dimensional case. (C) 1995 Academic Press, Inc.