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

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2010

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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
StatePublished

Conference

Conference15th European Conference on Mathematics for Industry
CountryUnited Kingdom
CityLondon
Period30/06/0804/07/08
Internet addresshttp://www.ima.org.uk/ecmi/
NameIndustrial Mathematics
CitationsWeb of Science® Times Cited: 0

Keywords

  • nonlinear partial differential equations, Thermoviscous shocks
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