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

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-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 languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2008
Place of PublicationHeidelberg, Dordrecht, London, New York
PublisherSpringer Verlag
Publication date2010
Edition1
Pages997-1002
ISBN (Print)978-3-642-12109-8
DOIs
Publication statusPublished - 2010
Event15th European Conference on Mathematics for Industry - University College London, London, United Kingdom
Duration: 30 Jun 20084 Jul 2008
http://www.ima.org.uk/ecmi/

Conference

Conference15th European Conference on Mathematics for Industry
LocationUniversity College London
CountryUnited Kingdom
CityLondon
Period30/06/200804/07/2008
Internet address
SeriesIndustrial Mathematics

Keywords

  • nonlinear partial differential equations
  • Thermoviscous shocks

Cite this

Rasmussen, A. R., Sørensen, M. P., Gaididei, Y. B., & Christiansen, P. L. (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 ed., pp. 997-1002). Heidelberg, Dordrecht, London, New York: Springer Verlag. Industrial Mathematics https://doi.org/10.1007/978-3-642-12110-4_159
Rasmussen, Anders Rønne ; Sørensen, Mads Peter ; Gaididei, Yuri Borisovich ; Christiansen, Peter Leth. / 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; Christiansen, Peter Leth.

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 proceedingArticle in proceedingsResearchpeer-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). https://doi.org/10.1007/978-3-642-12110-4_159