Saint Venant’s equations have no known analytical solution in real geometry. They are solved numerically by discretizing the equations: the partial derivatives are replaced by finite differences. Various solution schemes may be used to provide a solution to these equations. The discretization scheme chosen in the SIC model is a four-point semi-implicit scheme known as Preissmann’s scheme (Figure 26).

This scheme is implicit because the values of the variables at the unknown time step also appear in the expression containing spatial partial derivatives.