DISCRETE TRANSPARENT BOUNDARY-CONDITIONS FOR WIDE-ANGLE PARABOLIC EQUATIONS IN UNDERWATER ACOUSTICS

This paper is concerned with transparent boundary conditions (TBCs) fo r wide angle ''parabolic'' equations (WAPEs) in the application to und erwater acoustics (assuming cylindrical symmetry). Existing discretiza tions of these TBCs introduce slight numerical reflections at this art ificial boundary and also render the overall Crank-Nicolson finite dif ference method only conditionally stable. Here, a novel discrete TBC i s derived from the fully discretized whole-space problem that is refle ction-free and yields an unconditionally stable scheme. While we shall assume a uniform discretization in range, the interior depth discreti zation (i.e. in the water column) may be nonuniform, and we shall disc uss strategies for the ''best exterior discretization'' (i.e. in the s ea bottom). The superiority of the new discrete TBC over existing disc retizations is illustrated on several benchmark problems. In the liter ature different WAPEs (or WAPE and the standard ''parabolic'' equation ) have been coupled in the water and the sea bottom. We analyze under which conditions this yields a hybrid model that is conservative for t he acoustic held. (C) 1998 Academic Press.