Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation.

Anders Rønne Rasmussen; Mads Peter Sørensen; Yuri Borisovich Gaididei; Peter Leth Christiansen

doi:10.1007/978-3-642-12110-4_159

Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation.

Anders Rønne Rasmussen, Mads Peter Sørensen, Yuri Borisovich Gaididei, Peter Leth Christiansen

Department of Physics

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. The equation preserves the Hamiltonian structure of the fundamental fluid dynamical equations in the non dissipative limit. An exact thermoviscous shock solution is derived. This solution is, in an overall sense, equivalent to the Taylor shock solution of the Burgers equation. However, in contrast to the Burgers equation, the model equation considered here is capable to describe waves propagating in opposite directions. Studies of head on colliding thermoviscous shocks demonstrate that the propagation speed changes upon collision.

Original language	English
Title of host publication	Progress in Industrial Mathematics at ECMI 2008
Place of Publication	Heidelberg, Dordrecht, London, New York
Publisher	Springer Verlag
Publication date	2010
Edition	1
Pages	997-1002
ISBN (Print)	978-3-642-12109-8
DOIs	https://doi.org/10.1007/978-3-642-12110-4_159
Publication status	Published - 2010
Event	15th European Conference on Mathematics for Industry - University College London, London, United Kingdom Duration: 30 Jun 2008 → 4 Jul 2008 http://www.ima.org.uk/ecmi/

Conference

Conference	15th European Conference on Mathematics for Industry
Location	University College London
Country/Territory	United Kingdom
City	London
Period	30/06/2008 → 04/07/2008
Internet address	http://www.ima.org.uk/ecmi/

Series	Industrial Mathematics

Keywords

nonlinear partial differential equations
Thermoviscous shocks

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10.1007/978-3-642-12110-4_159

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Rasmussen, Anders Rønne ; Sørensen, Mads Peter ; Gaididei, Yuri Borisovich et al. / Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation. Progress in Industrial Mathematics at ECMI 2008. 1. ed. Heidelberg, Dordrecht, London, New York : Springer Verlag, 2010. pp. 997-1002 (Industrial Mathematics).

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abstract = "A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. The equation preserves the Hamiltonian structure of the fundamental fluid dynamical equations in the non dissipative limit. An exact thermoviscous shock solution is derived. This solution is, in an overall sense, equivalent to the Taylor shock solution of the Burgers equation. However, in contrast to the Burgers equation, the model equation considered here is capable to describe waves propagating in opposite directions. Studies of head on colliding thermoviscous shocks demonstrate that the propagation speed changes upon collision.",

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Rasmussen, AR, Sørensen, MP, Gaididei, YB & Christiansen, PL 2010, Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation. in Progress in Industrial Mathematics at ECMI 2008. 1 edn, Springer Verlag, Heidelberg, Dordrecht, London, New York, Industrial Mathematics, pp. 997-1002, 15th European Conference on Mathematics for Industry, London, United Kingdom, 30/06/2008. https://doi.org/10.1007/978-3-642-12110-4_159

Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation. / Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich et al.
Progress in Industrial Mathematics at ECMI 2008. 1. ed. Heidelberg, Dordrecht, London, New York: Springer Verlag, 2010. p. 997-1002 (Industrial Mathematics).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Rasmussen AR, Sørensen MP, Gaididei YB, Christiansen PL. Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation. In Progress in Industrial Mathematics at ECMI 2008. 1 ed. Heidelberg, Dordrecht, London, New York: Springer Verlag. 2010. p. 997-1002. (Industrial Mathematics). doi: 10.1007/978-3-642-12110-4_159

Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation.

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