A BICHARACTERISTICS METHOD FOR ADAPTIVE MODELING OF TRANSIENT WAVE PROPAGATION IN UNBOUNDED ACOUSTIC MEDIA

Abstract

A computational procedure is developed for adaptive modeling of transient wave propagation in an unbounded acoustic layer. The adaptivity herein is concerned with controlling the error caused by imperfect modeling of unbounded domains, and the procedure aims at determining the optimal order of the absorbing boundary condition (ABC) under consideration to control the error in the solution within a predetermined tolerance. The perfectly matched layer (PML) is used as an ABC, and the size of the PML domain controls the error associated with modeling unbounded domains. As a key technique in the adaptive method, a local solution procedure is designed based on the method of bicharacteristics to extract, from the computed solution, the information flowing into the computational domain. Numerical experiments show that, under wide circumstances, the maximum pressure associated with the inflow evaluated near the truncated boundary of the PML domain can be related with the maximum error in the pressure and thus can be used as an error estimator. It is demonstrated that a simple adaptive algorithm based on this error estimator can automatically determine the PML domain size to produce solutions with controlled errors.