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

Publication: Research - peer-review › Article in proceedings – Annual report year: 2010

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**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.

Publication: Research - peer-review › Article in proceedings – Annual report year: 2010

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*Progress in Industrial Mathematics at ECMI 2008.*1 edn, Springer Verlag, Heidelberg, Dordrecht, London, New York, pp. 997-1002. Industrial Mathematics, DOI: 10.1007/978-3-642-12110-4_159

### APA

*Progress in Industrial Mathematics at ECMI 2008.*(1 ed., pp. 997-1002). Heidelberg, Dordrecht, London, New York: Springer Verlag. (Industrial Mathematics). DOI: 10.1007/978-3-642-12110-4_159

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*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

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### RIS

TY - GEN

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

AU - Rasmussen,Anders Rønne

AU - Sørensen,Mads Peter

AU - Gaididei,Yuri Borisovich

AU - Christiansen,Peter Leth

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

M3 - Article in proceedings

SN - 978-3-642-12109-8

SP - 997

EP - 1002

BT - Progress in Industrial Mathematics at ECMI 2008

PB - Springer Verlag

ER -