Finite element and variational integration for water waves

202002_close_109 On Friday afternoon, 18 July, Elena Gagarina presented a talk on a combination of finite-element discretisation in space coupled to discontinuous symplectic integration in time.  The methodology starts with Miles’ re-formulation of Luke’s variational principle for irrotational gravity waves.  The functional is discretised directly in both space and time leading to a variational discretisation.  The main aim was to simulate a wave tank experiment involving waves generated at one end of a tank and propagating to the other end.  Comparison with experiments at MARIN showed excellent agreement.  A second experiment involved focussing, where the forcing introduce two distinct wavelengths.  When the longer wave overtakes the shorter wave focussing occurs as shown in the above figure.  The main symplectic integrator was second order in time.  A third order symplectic integrator was also derived which appears to be new.  A video of the talk is available here.

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