### Abstract

Original language | English |
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Title of host publication | Progress in Industrial Mathematics at ECMI 2008 |

Place of Publication | Heidelberg, Dordrecht, London, New York |

Publisher | Springer Verlag |

Publication date | 2010 |

Edition | 1 |

Pages | 997-1002 |

ISBN (Print) | 978-3-642-12109-8 |

DOIs | |

Publication status | Published - 2010 |

Event | 15th European Conference on Mathematics for Industry - University College London, London, United Kingdom Duration: 30 Jun 2008 → 4 Jul 2008 http://www.ima.org.uk/ecmi/ |

### Conference

Conference | 15th European Conference on Mathematics for Industry |
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Location | University College London |

Country | United Kingdom |

City | London |

Period | 30/06/2008 → 04/07/2008 |

Internet address |

Series | Industrial Mathematics |
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### Keywords

- nonlinear partial differential equations
- Thermoviscous shocks

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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

T3 - Industrial Mathematics

SP - 997

EP - 1002

BT - Progress in Industrial Mathematics at ECMI 2008

PB - Springer Verlag

CY - Heidelberg, Dordrecht, London, New York

ER -