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

Standard

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).

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

Harvard

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, pp. 997-1002. Industrial Mathematics, , 10.1007/978-3-642-12110-4_159

APA

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

CBE

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 ed. Heidelberg, Dordrecht, London, New York: Springer Verlag. pp. 997-1002. (Industrial Mathematics). Available from: 10.1007/978-3-642-12110-4_159

MLA

Rasmussen, Anders Rønne 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 udg., Heidelberg, Dordrecht, London, New York: Springer Verlag. 2010. 997-1002. (Industrial Mathematics). Available: 10.1007/978-3-642-12110-4_159

Vancouver

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). Available from: 10.1007/978-3-642-12110-4_159

Author

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. p. 997-1002 (Industrial Mathematics).

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

Bibtex

@inbook{1aa86ce82a83479dafc7975de1b2d0fb,
title = "Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation.",
keywords = "nonlinear partial differential equations, Thermoviscous shocks",
publisher = "Springer Verlag",
author = "Rasmussen, {Anders Rønne} and Sørensen, {Mads Peter} and Gaididei, {Yuri Borisovich} and Christiansen, {Peter Leth}",
year = "2010",
doi = "10.1007/978-3-642-12110-4_159",
edition = "1",
isbn = "978-3-642-12109-8",
series = "Industrial Mathematics",
pages = "997-1002",
booktitle = "Progress in Industrial Mathematics at ECMI 2008",

}

RIS

TY - GEN

T1 - Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation.

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

PB - Springer Verlag

CY - Heidelberg, Dordrecht, London, New York

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - nonlinear partial differential equations

KW - Thermoviscous shocks

U2 - 10.1007/978-3-642-12110-4_159

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

SN - 978-3-642-12109-8

BT - Progress in Industrial Mathematics at ECMI 2008

T2 - Progress in Industrial Mathematics at ECMI 2008

T3 - Industrial Mathematics

T3 - en_GB

SP - 997

EP - 1002

ER -