#### Document Type

Article

#### Publication Date

2017

#### DOI

10.1121/1.5017734

#### Publication Title

Journal of the Acoustical Society of America

#### Volume

142

#### Issue

6

#### Pages

3624-3636

#### Abstract

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source or sink points on solid surfaces. An alternative solid wall boundary condition, termed zero energy flux boundary condition, is proposed that conserves the acoustic energy and a time domain boundary integral equation is derived. Furthermore, stabilization of the integral equation by Burton-Miller type reformulation is presented. The stability is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the current formulation. *(C) 2017 Acoustical Society of America*.

#### Original Publication Citation

Hu, F. Q., Pizzo, M. E., & Nark, D. M. (2017). On a time domain boundary integral equation formulation for acoustic scattering by rigid bodies in uniform mean flow. *Journal of the Acoustical Society of America, 142*(6), 3624-3636. doi:10.1121/1.5017734

#### Repository Citation

Hu, Fang Q.; Pizzo, Michelle E.; and Nark, Douglas M., "On a Time Domain Boundary Integral Equation Formulation for Acoustic Scattering by Rigid Bodies in Uniform Mean Flow" (2017). *Mathematics & Statistics Faculty Publications*. 64.

https://digitalcommons.odu.edu/mathstat_fac_pubs/64

#### Included in

Acoustics, Dynamics, and Controls Commons, Applied Mathematics Commons, Mathematics Commons