where  denotes the distance of the barycenters between element  and satellite element 1.

 Eqs. (12) and (13) concern four satellite elements around the element , but the limiter function concerns another four satellite elements, so this scheme concerns eight satellite elements in all.

5.  BOUNDARY CONDITIONS

   The boundaries of the computational domain have land boundaries (solid boundaries) and water boundaries (open boundaries) for a general shallow water problem. In the case of solid boundaries, no-slip or slip boundary conditions is considered on the basis of whether considering turbulent viscosity or not. Generally speaking, no-slip boundary conditions are given if considering turbulent viscosity, otherwise slip conditions are specified. The open boundary conditions, however, need to have a particular treatment. The local value of Froude number or whether the flow is subcritical or supercritical is the basis of determining the number of boundary conditions. For supercritical flow, three conditions at the inflow boundary and none at the outflow boundary must specified. For subcritical flow, two external conditions are specified at inflow boundary and one is required at the outflow boundary.

  

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