A variational principle in terms of stream function for freesurface flows and its application to the finite element method
Abstract
Steady freesurface flows under the influence of gravity are considered in this paper. The appropriate variational principle is derived, where the stream function within the flow and the freesurface elevation are independently subjected to variation. The formulation of the principle in terms of linear finite elements is presented, and the resulting set of nonlinear equations is reduced to the iterative solution of a linear set. The computations are shown to be convergent regardless of whether the Froude number of the stream is greater or less than unity, and independent tests show that the accuracy of the results is well within the usual range expected for internal flows when linear elements are used.
 Publication:

Computers and Fluids
 Pub Date:
 June 1979
 Bibcode:
 1979CF......7..145B
 Keywords:

 Finite Element Method;
 Free Flow;
 Steady Flow;
 Stream Functions (Fluids);
 Variational Principles;
 Bernoulli Theorem;
 Flow Equations;
 Froude Number;
 Gravitational Effects;
 Green'S Functions;
 Iteration;
 Nonlinear Equations;
 Fluid Mechanics and Heat Transfer