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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.

### MSC:

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 |

### Keywords:

semi-implicit finite difference model; three-dimensional shallow water equations; unstructured grids; flooding; drying; convergence rates; river plain; shallow estuary
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\textit{V. Casulli} and \textit{R. A. Walters}, Int. J. Numer. Methods Fluids 32, No. 3, 331--348 (2000; Zbl 0965.76061)

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### References:

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