INCOH/SAR-22/2000-Application of finite element method to some flow problems

Abstract

During the past few decades, a significant number of research papers have appeared which apply the finite element technique to the solution of wide variety of problems in Hydraulic Engineering and Water Resources. These papers in general point out that the stability and a:curacy of the Finite Element models are comparable to those found in Finite Difference models. In some cases where complex geometries are involved, Finite Element models score well over Finite Difference models. The advent of computers also contributed to the development of Finite Element models to solve wide variety of engineering problems. Further improvement over FEM in recent years is the application of Boundary integral method to some engineering problems and it was claimed by Brebbia (1988) that it offers an excellent alternative to Finite Element for the solution of some practical problems. In BEM only the boundary is discretised and the solution is obtained in terms of boundary nodes. The values of field variables are evaluated using the fundamental solution associated with the governing equation. The size of the matrix formed is small compared to the FEM. However, the discussion will be restricted to the FEM only in this report. The report deals with the finite element formulation of some of the problems encountered in Hyd. Engg./Watcr Resources. These are mainly: (a) Water Distribution Networks,(b)Water Hammer Problems, (c)Dispersion of pollutants in aquifers, (d) Ground Water management, (e) Two-Dimensional Stream Flow modelling, (0 Surface Runoff modelling.