Numerical Modeling in Open Channel Hydraulics

Abstract

Open channel hydraulics has always been a very interesting domain of scientific and engineering activity because of the great importance of water for human living. The free surface flow, which takes place in the oceans, seas and rivers, can be still regarded as one of the most complex physical processes in the environment. The first source of difficulties is the proper recognition of physical flow processes and their mathematical description. The second one is related to the solution of the derived equations. The equations arising in hydrodynamics are rather complicated and, except some much idealized cases, their solution requires application of the numerical methods. For this reason the great progress in open channel flow modeling that took place during last 40 years paralleled the progress in computer technique, informatics and numerical methods. It is well known that even typical hydraulic engineering problems need applications of computer codes. Thus, we witness a rapid development of ready-made packages, which are widely disseminated and offered for engineers. However, it seems necessary for their users to be familiar with some fundamentals of numerical methods and computational techniques applied for solving the problems of interest. This is helpful for many reasons. The ready-made packages can be effectively and safely applied on condition that the users know their possibilities and limitations. For instance, such knowledge is indispensable to distinguish in the obtained solutions the effects coming from the considered physical processes and those caused by numerical artifacts. This is particularly important in the case of hyperbolic equations, like the Saint-Venant equations or the advection equation. In principle, numerical open channel hydraulics can be regarded as a sub-domain of Computational Fluid Dynamics (CFD) and the general methods and experiences of CFD are applicable in open channel flow modeling. Moreover, the open channel flow can be often treated as one-dimensional, which makes it relatively easy to solve compared to multidimensional flows considered in geophysics and industrial engineering. On the other hand, due to a range of specific issues, numerical open channel hydraulics developed into a branch of its own as early as in the years 1960s and 1970s. There exist a number of very good books on the subject, written at that time and later. A non-exhaustive list includes “Unsteady flow in open channel” edited by K. Mahmood and V. Yevjevich and containing the papers written by recognized