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Dynamic coupling between shallow-water sloshing and horizontal vehicle motion

Published online by Cambridge University Press:  07 July 2010

HAMID ALEMI ARDAKANI  and
THOMAS J. BRIDGES
HAMID ALEMI ARDAKANI
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK emails: H.Alemiardakani@surrey.ac.uk & T.Bridges@surrey.ac.uk
THOMAS J. BRIDGES
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK emails: H.Alemiardakani@surrey.ac.uk & T.Bridges@surrey.ac.uk
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Abstract

The coupled motion between shallow-water sloshing in a moving vehicle and the vehicle dynamics is considered, with the vehicle dynamics restricted to horizontal motion. The paper is motivated by Cooker's experiments and theory for water waves in a suspended container. A new derivation of the coupled problem in the Eulerian fluid representation is given. However, it is found that transformation to a Lagrangian representation leads to a formulation which has nice properties for numerical simulation. In the Lagrangian representation, a simple and fast numerical algorithm with excellent energy conservation over long times, based on the Störmer–Verlet method, is implemented. Numerical simulations of the coupled dynamics in both the linear and non-linear case are presented.

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 6 , December 2010 , pp. 479 - 517
Copyright
Copyright © Cambridge University Press 2010

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