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.
In: 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-review › Article in proceedings – Annual report year: 2010
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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 -