Ein numerisches Verfahren zur Errechnung von Windstau und Gezeiten in Randmeeren

Abstract

A finite difference method for determining water heights and movements in adjacent seas is developed. For this purpose the vertically integrated equations of motion and the continuity equation are transformed into an explicit system of difference equations, which are solved stepwise in time with an electronic computer. The question of numerical stability is investigated in detail. To obtain computational stability for the system in question, it is not sufficient to satisfy a condition similar to the Courant Friedrichs Lewy criterion, as there is also an upper limit of the timestep itself, which depends on the frictional coefficient and the boriolis parameter. The influence of a smoothing technique and the mesh size of the grid on the results is also examined. Some computations of storm surges and tides in the North Sea are presented and are compared in selected cases with the results of other methods or with observations. The computations of tidal waves and currents in the North Sea, where the wave was prescribed only at the open ends, give a reasonable agreement with observed conditions. DOI: 10.1111/j.2153-3490.1959.tb00005.x