(1b)

where h is water depth,  are the discharges per unit width, bottom slopes and friction slopes along x- and y- directions respectively. The friction slopes  and are determined by Manning’s formula

                             (2)

in which n is Manning roughness coefficient.

 

　

　

Fig. 1.  Geometric and topological relationship between elements

Fig. 2  Relationship between elements  on land boundaries

3.      GEOMETRICAL AND TOPOLOGICAL RELATIONSHIPS OF ELEMENTS

   The second-order TVD schemes belong to five-point finite difference scheme and the unsolved variables are node-node arrangement. In order to extend them to the finite volume method, it is necessary to define the control volume. The types of traditional control volume have element itself, such as triangle, quadrilateral and other polygons or some kinds of combinations, and polygons made up of the barycenters from the adjacent elements. In this paper we consider that a

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