Simulation of flow in rivers and tidal channels with an implicit finite difference method of the ADI-type

Abstract

In order to make predictions for the morphology of an alluvial bottom a thorough knowledge of the flow pattern is needed. In tidal channels, without a nett discharge over the tidal period, the main flow effects on the morphology will, on an average, remain relatively small because of the tidal variation. Therefore second order flow phenomena become important. In particular the secondary flow is important, because it gives rise to bottom slopes transverse to the main flow. This research, which is financially supported by the directorate of the Deltadienst of Rijkswaterstaat, concerns the determination of the secondary flow in tidal channels like estuaries as the Eastern Scheldt based on a known depth averaged velocity field. The depth averaged velocities must be computed with a high accuracy in order to make a reasonable determination of the secondary flow. For the computation of depth averaged velocities usually an implicit finite difference method of the ADI-type is used. In these methods the depth averaged equations of motion, together with the depth averaged continuity equation, together called the shallow water equations, are solved by means of an Alternating Direction Implicit computation using a spatial staggered grid. A simplification of the effective stress term in the shallow water equations is made to economize the computation. Although the velocity parameters and water level parameter are treated implicitly, the convective and diffusion terms are represented explicitly in the difference equations, which can give rise to instability of the numerical computation. The computation is executed with an imposed diffusion coefficient in order to suppress this instability. In this report an investigation is done concerning the diffusion coefficient and its influence on the velocity distribution in a steady or quasi-steady flow in rivers and estuaries. Estimates of the physical lateral viscosity for the same flows are made and their influence on the velocity distribution is discussed.