Numerical method of location of free water surface and water table

In the process of obtaining analytical solutions for hydrodynamic equations in free surface flow problems, the most common difficulty lies in the location of free surface. Similar difficulties are encountered in ground water problems, where water table becomes one of the boundaries. In these two types of problems encountered above, the governing equations are of similar nature, but the free boundary conditions are different. Numerical solution of typical problem of steady flow under a sluice gate with a free surface on upstream and downstream are obtained. Also the problem of steady seepage under a sheet pile with a free surface on the upstream and water table on the downstream is solved. The difficulties in obtaining the Numerical solution in both the cases are compared and explained. Finite Element Method (FEM) is adopted using linear and higher order elements, wherever required. Free surface adjustments are made over the whole domain containing the free surface to avoid coarsening or overlapping of elements connected with the free surface. This process is made applicable to the seepage problem also. Experimental solutions involving electrical analogue for the seepage problem, with a provision to simulate a trial water table, are also attempted. Comparison of numerical and experimental results are found satisfactory.