Comparison of numerical methods solving flow through porous media

Ein Vergleich von numerischen Verfahren zur Lösung von Sickerstrümungen

Lehrgebiet Landwirtschaftlicher Wasserbau, Universität Karlsruhe, 75 Karlsruhe (West-Germany)

Abstract

The development of groundwater models solving actual engineering problems is of great interest as well with regard to physical as with regard to economical aspects. These models enable a more precise treatment of problems during the stage of planning. Furthermore, these models assure a permanent control of finished steps. Generally, the flow through porous media is a three-dimensional process depending on various parameters. Normally, this process is so complicated that it is not possible to describe the situation in nature in a general form. Therefore, it is necessary to develop some simplified physical models of groundwater flow which are adapted to relevant individual circumstances. These refer for example to steady or unsteady flow, to flow with or without a free surface, to flow in an isotropic or anisotropic aquifer, to one-, two- or three-dimensional flow. The solution of these different physical models can be obtained by use of analytical, analog or digital methods, which consider the typical physical conditions. Such a concept of a physical model and a corresponding solution method is to be defined as a socalled analytical, analog or digital flow model through porous media. As the organization of flow models through porous media causes generally high costs, which c1epend mainly on the choice of the solution method, it is of great interest, which of the different solution methods is suitable for a given problem. It was possible to prove by a cost-effectiveness-analysis, that digital solution methods generally are considerably more effective than analytical and analogous methods. As digital solution methods, one can use either the method of finite elements or the method of finite differences. Both methods produce discrete solutions of given problems. The comparison of both methods is to be done by significant criteria. These are: 1. the required core storage; 2. the required computing time; 3. the flexibility of the methods approximating the problems. As the core storage and the computing time c1irectly depend on the organization technique and the algorithm solving linear equation systems, special organization techniques are to be discussed. The flexibility is to be seen in clependence on physical problems. The comparison of both methods (methods of finite elements and finite differences, respectively) shows, that the method of finite differences is much more better with regard to organization and programming aspects, especially however, with regard to economical aspects (Jess required core storage, less computing time). In general, flow problems through porous media should be solved by the method of finite differences. For all problems, however, which involve an automatic search of free surfaces, the method of finite elements appears to be more suitable, because only its organization can realize these problems.