A source term approach for generation of one-way acoustic waves in the Euler and Navier–Stokes equations

Abstract

We derive a volumetric source term for the Euler and Navier–Stokes equations that mimics the generation of unidirectional acoustic waves from an arbitrary smooth surface in three-dimensional space. The model is constructed as a linear combination of monopole and dipole sources in the mass, momentum, and energy equations. The singular source distribution on the surface is regularized on a computational grid by convolution with a smeared Dirac delta function. The source is implemented in the Euler equation using a Cartesian-grid finite-volume WENO scheme, and validated by comparing with analytical solution for unidirectional planar and spherical acoustic waves. Using the scheme, we emulate a spherical piezoelectric transducer and a multi-element array medical transducer to simulate focused ultrasound fields in water. The simulated ultrasound fields show favorable agreement with previous experiments.