Interacting Wave Fronts and Rarefaction Waves in a Second Order Model of Nonlinear Thermoviscous Fluids |
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Authors: | Anders Rønne Rassmusen Mads Peter Sørensen Yuri Borisovich Gaididei Peter Leth Christiansen |
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Institution: | 1.Department of Mathematics,Technical University of Denmark,Kongens Lyngby,Denmark;2.IRD Fuel Cells,Svendborg,Denmark;3.Bogolyubov Institute for Theoretical Physics,Kiev,Ukraine;4.Department of Informatics and Department of Physics,Technical University of Denmark,Kongens Lyngby,Denmark |
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Abstract: | 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. |
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