Three-dimensional irregular-grid finite difference model of wind induced water level fluctuations and currents in a homogeneous lake with applications to the lake of Geneva
Combining the neat representation of boundary geometry of finite element models with the advantage of fast numerical solution of finite difference models, an irregular-grid finite difference scheme was developed to solve the hydrodynamic equations of motion in a three-dimensional homogeneous lake. The operation of the model was first demonstrated by applying it in a one- and a three-layer formulation to a lake of arbitrary shape. With an initially coarse irregular grid, the model was then used to simulate water level fluctuations observed in the Lake of Geneva (Le Léman) during a 60-hour episode of strong north-easterly winds. It was found that numerical instabilities arising from the use of a completely irregular finite-difference grid can be largely eliminated if the grid is modified in such a way that each interior grid point is placed centrally with respect to all surrounding points. With a "smoothed-irregular" grid scheme, modified in this way, it was possible to reproduce in considerable detail the water level responses observed by Forel and others in the Léman, i.e., the surges generated by wind stress and the free oscillations (seiches) which follow.