Free-Surface Ideal Fluid Flows by Finite Elements

The two dimensional flow of an ideal fluid which emerges as a free surface jet from a containing vessel of arbitrary shape is studied. The finite element analysis of this problem seeks an approximate solution for the minimization of a functional which describes this problem. Gravity effects and curvilinear, solid boundary walls are easily taken into account. The method provides a rational analytical algorithm for adjusting free surface coordinates. The iterative technique used in conjunction with the algorithm requires the solution of a linear, symmetric, banded equation system during each iteration, which is quickly done by Gaussian elimination. Results include not only free surface profiles but also velocity and pressure distributions throughout the flow domain. Computational examples are given which required 10-20 iterations and used 3 to 8 min of execution time on the IBM 7044 computer.