The symmetry and stability of unstructured mesh C-grid shallow water models under the influence of Coriolis |
| |
| Institution: | 1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran;2. Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Makassar, Indonesia;1. Department of Human Health and Nutritional Sciences, University of Guelph, Guelph, ON, Canada;2. Department of Graduate Education and Research Programs, Canadian Memorial Chiropractic College, Toronto, ON, Canada;3. School of Human Kinetics, University of Ottawa, Ottawa, ON, Canada |
| |
| Abstract: | The symmetry and stability properties of two unstructured C-grid discretisations of the shallow water equations are discussed. We establish that a scheme in which the circumcentres of the mesh triangles are used as the surface elevation points has advantageous symmetry properties and derive a Coriolis discretisation which preserves these properties. It is shown that the resulting scheme is conservative in a discretised energy norm. We then establish that schemes in which the water surface elevations are stored at the mesh triangle centroids do not share these advantageous symmetry properties. Finally we show examples which demonstrate that the centroid based scheme is subject to unstable growing modes, particularly in long timescale, Coriolis dominated problems; while the energy conservative circumcentre based scheme suffers from no such limitation. We conclude that unstructured C-grid methods using the triangle circumcentres and the conservative Coriolis scheme derived here therefore have advantages for this sort of problem over those schemes based on centroids. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
