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Method of moving frames to solve the shallow water equations on rotating arbitrary curved surfaces

Sehun Chun ; Claes Eskilsson (Institutionen för sjöfart och marin teknik, Marin teknik)
Journal of Computational Physics (0021-9991). Vol. 333 (2017), p. 1-23.
[Artikel, refereegranskad vetenskaplig]

A novel numerical scheme is proposed to solve the shallow water equations (SWEs) on arbitrary rotating curved surfaces. Based on the method of moving frames (MMF) in which the geometry is represented by orthonormal vectors, the proposed scheme not only has the fewest dimensionality both in space and time, but also does not require either of metric tensors, composite meshes, or the ambient space. The MMF–SWE formulation is numerically discretized using the discontinuous Galerkin method of arbitrary polynomial order pin space and an explicit Runge–Kutta scheme in time. The numerical model is validated against six standard tests on the sphere and the optimal order of convergence of p +1 is numerically demonstrated. The MMF–SWE scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid, irregular, and non-convex surfaces.



Denna post skapades 2017-01-03. Senast ändrad 2017-03-31.
CPL Pubid: 246612

 

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Institutioner (Chalmers)

Institutionen för sjöfart och marin teknik, Marin teknik (2015-2017)

Ämnesområden

Beräkningsmatematik
Marin teknik

Chalmers infrastruktur