Numerical solution of the wave equation describing acoustic scattering and propagation through complex dispersive moving media

Abstract

The numerical solution of acoustic pulse propagation through dispersive moving media requires the inclusion of attenuation and its causal companion, phase velocity. For acoustic propagation in a linear medium, Szabo [T.L. Szabo, J. Acoust. Soc. Am. 96 (1994) 491] introduced the concept of a convolutional propagation operator that plays the role of a casual propagation factor in the time domain. This operator was originally proposed to replace the term responsible for including losses from thermal conduction and viscosity of the fluid in the Westervelt equation. The operator has been successfully used in the linear wave equation for quiescent media. Development of the linear wave equation for sound in dispersive fluids with inhomogeneous flow will be described, along with a one-dimensional example. The resulting modified linear wave equation is solved via the method of finite differences.