Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generelized Westervelt equation

MD Verweij, J Huijssen

    Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review


    In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.
    Original languageUndefined/Unknown
    Title of host publicationinnovations in nonlinear acoustics
    EditorsAA Atchly, VW Sparrow, RM Keolian
    Place of PublicationNew York
    PublisherAmerican Institute of Physics
    Number of pages4
    ISBN (Print)0-7354-0330-9
    Publication statusPublished - 2006
    Eventinnovations in nonlinear acoustics
    - New York
    Duration: 18 Jul 200522 Jul 2005

    Publication series

    PublisherAmerican Institute of Physics


    Conferenceinnovations in nonlinear acoustics


    • conference contrib. refereed
    • Conf.proc. > 3 pag

    Cite this