Problem definition

The equation to be solved has the following form:

  $$\frac{\partial}{\partial x_{k}}(F_{k} + gd \frac{\partial \zeta}{\partial x_{k}}) = 0\;,$$ (5.4)

In order to solve (5.4), the following types of boundary conditions may be applied

  $$F_{n} + gd \frac{\partial \zeta}{\partial n} = 0 \;\;\;\mbox{at the boundary}\;,$$ (5.5)

with $n$ the outward direct normal. This is a Neumann condition. The setup is fixed upon an additive constant.

  $$\zeta =\; \mbox{given at the boundary}\;.$$ (5.6)

This is boundary condition of Dirichlet type. At beaches always the Neumann condition (5.5) is applied.


In order to solve (5.4) with boundary conditions (5.5) and (5.6) a boundary fitted, vertex centered finite volume method is applied. In the remainder of this Chapter we use $k$ instead of $gd$.