An electromagnetic finite difference time domain analog treatment of small signal acoustic interactions

Abstract

Hyperbolic partial differential equations encompass an extremely important set of physical phenomena including electromagnetics and acoustics. Small amplitude acoustic interactions behave much the same as electromagnetic interactions for longitudinal acoustic waves because of the similar nature of the governing hyperbolic equations. Differences appear when transverse acoustic waves are considered, nonetheless the strong analogy between the acoustic and electromagnetic phenomena prompted the development of a Finite Difference Time Domain (FDTD) acoustic analog to the existing electromagnetic FDTD technique. The advantage of an acoustic FDTD (AFDTD) code are as follows: (1) Boundary condition-free treatment of the acoustic scatterer -- only the intrinsic properties of the scatterer`s material are needed, no shell treatment or other set of special equations describing the macroscopic behavior of a sheet of material or a junction, etc. are required; this allows completely general geometries and materials in the model. (2) Advanced outer radiation boundary condition analogs -- in the electromagnetics arena, highly absorbing outer radiation boundary conditions have been developed that can be applied with little modification to the acoustics arena with equal success. (3) A suite of preexisting capabilities related to electromagnetic modeling -- this includes automated model generation and interaction visualization as its most important components and is best exemplified by the capabilities of the LLNL generated TSAR electromagnetic FDTD code.