SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Compatible Space-Time Finite Element Discretizations for Wave Tanks

O. Bokhove, E. Gagarina and J.v.d. Vegt

The numerical modeling of nonlinear waves is often adequately done using conservative, Hamiltonian fluid dynamics, even in the presence of some forcing and damping. For two laboratory experiments such a non-autonomous Hamiltonian/variational framework is relevant: a) maritime engineering tests investigating rogue wave formation, also in model wave tanks, and b) wave-sloshing validations in a table-top Hele-Shaw cell with breaking waves. Wave-makers and linear momentum damping make these otherwise autonomous systems non-autonomous. We developed a compatible time-discontinuous Galerkin finite element discretization of geometric/variational dynamics. These discretizations are based on using a non-conservative product flux for the classical p dq/dt-term in the canonical variational principle. The challenge of finding compatible schemes for certain (forced/damped) fluid systems in space and time will also be highlighted.

Organized by         Universidad de Valladolid     IMUVA