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Cumulative Nonlinear Effects in Acoustic Wave Propagation

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

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

Computer Modeling in Engineering & Sciences 2007, 17(1), 47-54.


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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Christov, I., Christov, C., Jordan, P. (2007). Cumulative Nonlinear Effects in Acoustic Wave Propagation. CMES-Computer Modeling in Engineering & Sciences, 17(1), 47–54.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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