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An unstructured grid three-dimensional model based on the shallow water equations. (English) Zbl 0965.76061
Summary: A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model conserves mass, can fit complicated boundaries, and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary.

76M20 Finite difference methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
Full Text: DOI
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