Method of moving frames to solve the shallow water equations on rotating arbitrary curved surfaces
Journal article, 2017

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.

Author

Sehun Chun

Yonsei University

Claes Eskilsson

Chalmers, Shipping and Marine Technology, Marine Technology

Journal of Computational Physics

0021-9991 (ISSN) 1090-2716 (eISSN)

Vol. 333 1-23

Subject Categories

Computational Mathematics

Marine Engineering

DOI

10.1016/j.jcp.2016.12.013

More information

Created

10/7/2017