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First the momentum equations are rewritten as

  (1)

where includes all other terms. The equation is then integrated over the a control volume as

  (2)

The resulting di


The continuity equation is discretized as


where the subscript indicates the cell face, with being the water surface elevation, is equal to the dot product of the velocity unit vector and the cell face unit vector.

The coefficient is equal to

The continuity equation is discretized as

where is the dot product of the cell face unit vector and


The depth-averaged 2-D continuity and momentum equations are given by

  (1)

for