Bokhove lectures on variational principles, water waves and discretization

PlungingWaveFrame430bOnno Bokhove began his talk at the summer school by showing a demonstration of wave breaking in a Hele-Shaw cell.  A snapshot of a similar demonstration is shown to the left.  A variational principle and Hamiltonian formulation for the Hele-Shaw model was derived including weak dissipation and forcing.  The non-autonomy was handled by lifting the the Hamiltonian formulation to a Kamiltonian formulation.  A discretization based on discontinuous Galerkin in space, with symplectic integration in time was introduced, including a new third order symplectic time-integration scheme.  Numerical error tests, comparisons with the experiment as well as comparisons with wave tank experiments at MARIN were presented. Background material for the talk includes Gagarina, Ambati, van der Vegt, & Bokhove (2014) and Thornton, van der Horn, Gagarina, Zweers, van der Meer, & Bokhove (2014).  The slides from the lectures are available for downloading here. Lecture notes will be forthcoming.

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