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Burgers equation and convexification method: Propagation of wave packets and narrowband noise

Abstract : The Burgers equation is a standard model for the propagation of progressive finite amplitude waves in a lossy medium. This paper is mainly devoted to the one-dimensional Burgers equation and its solution deduced from a convexification method. Its starting point is the Hopf-Cole solution in the inviscid limit, then the Legendre-Fenchel transform and the convex envelope construction are employed to obtain the single-value waveform. A fractional step method is used to numerically solve the Burgers equation in a segregated manner (nonlinearity and dissipation). Numerical results are obtained for nonlinear propagation of a wave packet with a Gaussian envelope and a narrowband noise (deterministic and non-deterministic signals). The convexification method provides a tool to solve the problems of nonlinear propagation, especially in the case of noise propagation with the formation and interaction (coalescence) of a large number of discontinuities (shocks).
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https://hal-univ-lemans.archives-ouvertes.fr/hal-03614354
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Soumis le : dimanche 20 mars 2022 - 12:19:22
Dernière modification le : lundi 21 mars 2022 - 03:32:52

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Philippe Béquin. Burgers equation and convexification method: Propagation of wave packets and narrowband noise. Journal of the Acoustical Society of America, Acoustical Society of America, 2022, 151 (2), pp.1223-1234. ⟨10.1121/10.0009578⟩. ⟨hal-03614354⟩

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