Thursday 11 Jan 2018Hamiltonian Formulation of the Rotating Shallow Water Equations using split Exterior Calculus.

Dr Werner Bauer - Imperial College London

Streatham Court B 14:30-15:30

We present a novel formulation of the rotating shallow water equations in Hamiltonian form, using twisted differential forms. This is a natural extension of Bauer (2016), and provides a clean basis for the topological - metric split employed in that paper: the Hamiltonian encodes the metric information, while the Poisson brackets are purely topological. Using this new continuous formulation, a general discrete exterior calculus based numerical scheme is developed. It is shown that the TRiSK family of schemes (cf. Ringler et al. (2010), Thuburn et al. (2009)) is one particular example of the general scheme. This completes the characterization of TRiSK as a DEC scheme started in Thuburn & Cotter (2012) and further in Eldred & Randall (2017), by providing an understanding of all the operators that appear in terms of discrete versions of fundamental exterior calculus operators: the Hodge star, the wedge product and the exterior derivative. It is believed that this new understanding of TRiSK as a complete DEC scheme will provide a pathway to overcoming the accuracy issues of TRiSK on quasi-uniform spherical grids in a way that does not destroy its key properties. This is the subject of future work.

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