Numerical methods for weak shock propagation and diffraction around a microphone.

Abstract

There are two interrelated goals for this presentation. The first goal is to give an overview of available numerical approaches for weak shock propagation. There are multiple approaches available, including formulations based on the Burgers equation, KZK or NPE equations, the second-order equations of nonlinear acoustics, the Navier-Stokes equations, or the Boltzmann equation. There are also multiple numerical techniques for discretizing each of underlying equations, and while some approaches give special treatment to weak shocks others handle the shocks automatically. The second goal of this presentation is to show recent simulation results for an explosion shock interacting in two dimensions with a microphone. The diffraction of the weak shock around the microphone housing does turn out to be amplitude dependent. It is only a modest effect, increasing for higher amplitudes. This knowledge is important for precise, close-range blast source characterization. In the future, the nonlinear diffraction of weak shocks around transducers also should be investigated for finite amplitude biomedical ultrasound, since the mechanisms for nonlinear diffraction are almost identical for ultrasound and explosion waves. [Work supported by U.S. Army ERDC-CERL.]