Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves

JOURNAL OF COMPUTATIONAL PHYSICS

卷:275

Article

Gagarina, E.¹  Ambati, V. R.¹  van der Vegt, J. J. W.¹  Bokhove, O.^1,2 

[1] Univ Twente, Dept Appl Math, Math Computat Sci Grp, NL-7500 AE Enschede, Netherlands

[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

关键词: Nonlinear water waves;    Finite element Galerkin method;    Variational formulation;    Symplectic time integration;    Deforming grids;   

DOI  :  10.1016/j.jcp.2014.06.035

来源: Elsevier

【 摘 要 】

A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time. One novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis-a-vis the mesh deformation being geometrically dependent on free surface evolution. Another key feature is the use of a variational (dis) continuous Galerkin finite element discretization in time. Moreover, in the absence of a wave maker, it is shown to be equivalent to the second order symplectic Stormer-Verlet time stepping scheme for the free-surface degrees of freedom. These key features add to the stability of the numerical method. Finally, the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the Maritime Research Institute Netherlands. (C) 2014 Published by Elsevier Inc.

【 授权许可】

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