Open Access

ARTICLE

Cumulative Nonlinear Effects in Acoustic Wave Propagation

by Ivan Christov¹, C.I. Christov², P.M. Jordan³

1 Department of Mathematics, Texas A&M University, Col-lege Station, TX 77843-3368, USA
2 Department of Mathematics, University of Louisiana at Lafayette, LA 70504-1010, USA
3 Code 7181, Naval Research Laboratory, StennisSpace Center, MS 39529–5004, USA. E-mail: pjor-dan@nrlssc.navy.mil

Computer Modeling in Engineering & Sciences 2007, 17(1), 47-54. https://doi.org/10.3970/cmes.2007.017.047

Abstract

Two widely-used weakly-nonlinear models of acoustic wave propagation --- the inviscid Kuznetsov equation (IKE) and the Lighthill--Westervelt equation (LWE) --- are investigated numerically using a Godunov-type finite-difference scheme. A reformulation of the models as conservation laws is proposed, making it possible to use the numerical tools developed for the Euler equations to study the IKE and LWE, even after the time of shock-formation. It is shown that while the IKE is, without qualification, in very good agreement with the Euler equations, even near the time of shock formation, the same cannot generally be said for the LWE.

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