Hamiltonian Discontinuous Galerkin Finite Element Method for Internal Gravity Waves

An exactly energy conserving discretization

Master thesis (2015)

Authors

A.M. Van Oers

Contributors

L.R.M. Maas (mentor)

D.R. Van der Heul (mentor)

Department

Numerical analysis () (TU Delft)

Discretization Euler equations Fluid dynamics Hamiltonian dynamics DGFEM Internal gravity waves Wave attractor Energy conserving Structure preserving Phase space

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Published Date

26-03-2015

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Numerical analysis

Abstract

A DGFEM discretization has been developed for the Hamiltonian dynamics of stratified incompressible linear fluid flow. The developed discretization can handle the numerical challenges posed by wave attractors: the three dimensionality of the domain, the focusing of wave energy and the incompressibility of the flow. The discretization is unconditionally stable. The conservation of phase space and energy ensure that the numerical error is physically more correct since an unphysical numerical error that changes the total energy is not possible.

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