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@article{f8de9148028444a98abb81a79c070127,
title = "Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves",
keywords = "Wave fronts, Collective coordinate approach, Traveling wave analysis, Rarefaction waves, The Kuznetsov equation",
author = "Rasmussen, {Anders Rønne} and Sørensen, {Mads Peter} and Gaididei, {Yuri Borisovich} and Christiansen, {Peter Leth}",
year = "2011",
doi = "10.1007/s10440-010-9581-7",
volume = "115",
number = "1",
pages = "43--61",
journal = "Acta Applicandae Mathematicae",
issn = "01678019",

}

RIS

TY - JOUR

T1 - Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves

A1 - Rasmussen,Anders Rønne

A1 - Sørensen,Mads Peter

A1 - Gaididei,Yuri Borisovich

A1 - Christiansen,Peter Leth

AU - Rasmussen,Anders Rønne

AU - Sørensen,Mads Peter

AU - Gaididei,Yuri Borisovich

AU - Christiansen,Peter Leth

PY - 2011

Y1 - 2011

N2 - A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions as well as head-on colliding and confluent wave fronts exhibit several nonlinear interaction phenomena. These include wave fronts of changed velocity and amplitude along with the emergence of rarefaction waves. An analysis using the continuity of the solutions as well as the boundary conditions is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.

AB - A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions as well as head-on colliding and confluent wave fronts exhibit several nonlinear interaction phenomena. These include wave fronts of changed velocity and amplitude along with the emergence of rarefaction waves. An analysis using the continuity of the solutions as well as the boundary conditions is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.

KW - Wave fronts

KW - Collective coordinate approach

KW - Traveling wave analysis

KW - Rarefaction waves

KW - The Kuznetsov equation

U2 - 10.1007/s10440-010-9581-7

DO - 10.1007/s10440-010-9581-7

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

SN - 01678019

IS - 1

VL - 115

SP - 43

EP - 61

ER -