A NEW TOPOGRAPHY ADAPTED MESH REFINEMENT FOR 2D UNSTEADY SHALLOW WATER FLOW SIMULATIONS OVER DRY BEDS

摘要

In two dimensional hydraulic free surface problems, when a mesh is required to be representative of some topography, as the number of cells used to create the mesh increases, the discrete representation of the real problem improves, so the accuracy of the results is enhanced, but the computing time grows and this can be a cumbersome difficulty. On the other hand, the experience says that, when the topography is smooth, larger cells can be used to simulate a flooding event but, if the topography is highly irregular, the number of cells must be increased in order to allow for a correct flow representation. One solution is to generate a mesh with local refinement, in order to reduce the calculation effort and, at the same time, be able to achieve the accuracy in the flow simulation results that a globally fine mesh would provide. When cuadrilateral structured meshes are used, the refinement must be done in all cells contained in the rows and columns connected with the area whose cell-density we want to increase. Unstructured triangular meshes with local mesh refinement can lead to directional cell deformation depending on how they are created, and the grid refinement procedure is more complicated. The solution proposed here consists of using a structured triangular mesh of variable density following the variation of the bed slope. This produces a grid where the local refinement is introduced in the irregular topography zones, with a refinement depending on how irregular the topography is. Furthermore, the new cells are generated following a simple algorithm, without distortions and not affecting the size of the cells in the same row or column far from the area of interest. The performance and efficiency of a finite volume upwind method on different grids will be presented and compared for a river flow simulation problem over dry bed.