A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation

• Published in: Wave motion Vol. 58; pp. 180 - 195
• Main Authors: Velasco-Segura, R, Rendon, P L
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2015
• Subjects: Dissipation; Exact solutions; Finite volume method; GPU; High intensity focused ultrasound; Licenses; Logic; Mathematical analysis; Mathematical models; Nonlinearity; Source code; Westervelt equation; Westervelt equation; Finite volume method; High intensity focused ultrasound; GPU; 76Q05; 76M12
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2015.05.006

A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional finite volume method using the Roe linearization was implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a High Intensity Focused Ultrasound (HIFU) system, both with satisfactory results. The code, available under an open source license, is written for parallel execution on a Graphics Processing Unit (GPU), thus improving performance by a factor of over 60 when compared to the standard serial execution finite volume code CLAWPACK 4.6.1, which has been used as reference for the implementation logic as well. •Conservation laws consistent with the Westervelt equation are presented.•Finite Volume method is implemented and verified for these conservation laws.•High efficiency is achieved using GPU implementation.