Direction-Independent Algorithm for Simulating Nonlinear Pressure Waves
Publication: Journal of Engineering Mechanics
Volume 143, Issue 4
Abstract
This study formulates a frequency-domain computational scheme for simulating nonlinear wave propagation in a homogeneous medium governed by the Westervelt equation. The need for such numerical treatment arises in both engineering and medical imaging applications, where finite-amplitude pressure waves trigger nonlinear effects that may critically affect the sensory data. The primary advantage of the proposed approach over commonly used approximations, which account for nonlinear effects via the Burgers’ equation, lies in its ability to handle nonlinearities due to arbitrarily inclined incident waves, which becomes especially important for focused sound beams with large apertures, i.e., wide ranges of inclination angles. The proposed direction-independent algorithm has a direct mathematical connection with the Westervelt equation, as opposed to the Burger’s equation (that relies on the plane-wave hypothesis), and has computational efficiency that is comparable to that of the traditional approach. The developments are illustrated by numerical examples that verify the method against an analytical solution and highlight the significance of accurately modeling nonlinear waves.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 4 • April 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Apr 25, 2016
Accepted: Sep 15, 2016
Published online: Jan 27, 2017
Published in print: Apr 1, 2017
Discussion open until: Jun 27, 2017
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