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A Lagrangian Finite Element Treatment of Transient Gravitational Waves in Compressible Viscous Fluids

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In this paper the problem of transient gravitational wave propagation in a viscous compressible fluid is investigated. The problem is formulated in the Lagrangian description and is solved numerically by a finite element method. In computations either fixed in space or moving meshes that follow the material fluid particles are used with the purpose to compare their numerical performance. As illustrations, results of numerical simulations carried out for plane flows in a domain of simple geometry are presented. First, the finite element results are compared with available experimental data for the case of small-amplitude waves in order to validate the numerical model. Then, the problem of large-amplitude transient water wave propagation over a horizontal bottom, involving the wave reflection at a rigid wall, is considered. For the flow parameters typical of a laboratory flume, the evolution of the free-surface elevation and the time variations of the surface displacements at chosen locations are shown for a range of different moving wall amplitudes and excitation times.
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Bibliogr. 24 poz., il.
  • Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-328 Gdańsk, Poland,
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