TiAS ,„„^ 



At = —rr- (23) 



where V is the largest flow velocity to be encountered at a cell with its 

 smallest side length AS . The parameter n is of order 1. Therefore, the 

 time-step is constrained by the smallest cell width which contains the highest 

 flow velocity. In physical terms. Equation 23 requires that the flow cannot 

 move substantially farther than one cell width in one time-step. 

 Boundary conditions 



20. WIFM allows a variety of boundary conditions to be specified, which 

 can be classified into three groups: open boundaries, land-water boundaries, 

 and thin-wall barriers. 



21. Open boundaries. When the edge of the computational grid is 

 defined as water, such as a seaward boundary or a channel exiting the grid, 

 either the water elevation or the flow velocities can be specified as an open 

 boundary-condition. This information can be input to WIFM as tabular data, or 

 constituent tides can be calculated within the model during the time-stepping 

 process. 



22. Land-water boundaries. WIFM allows land-water boundaries to be 

 either fixed or variable to account for flooding in low-lying terrain. Fixed 

 boundaries specify a no-flow condition at the cell face between land and 

 water. The position of a variable boundary is determined by the relationship 

 of the water elevation at a "wet" cell to the land elevation at a neighboring 

 "dry" cell. Once a water elevation rises above the level of adjacent land 

 height, water is initially moved onto the "dry" cell by using a broad-crested 

 weir formula (Reid and Bodine 1968). When the water level on the dry cell 

 exceeds some small value, the boundary face is treated as open, and computa- 

 tions for n , u , and v are made at the now "wet" cell. Drying is the 

 inverse process, and mass is conserved in these procedures. 



23. Thin-wall barriers. These barriers are defined along cell faces 

 and are of three types: exposed, submerged, and overtopping. Exposed 

 barriers allow no flow across a cell face. Submerged barriers control flow 

 across a cell face by using a time-dependent friction coefficient. Overtop- 

 ping barriers are dynamic. They can be completely exposed, completely sub- 

 merged, or they can act as broad-crested weirs. The barrier character is 

 determined by its height and the water elevations in the two adjoining cells. 



20 



