Three-Dimensional Finite Element Model for Lake Circulation

Abstract:
A solution technique is presented for the three- dimensional (3- D) circulation of water in shallow lake basins. The basis for solution is a finite element analogue to the shallow lake equations due to Eckman. Galerkin's method provides the minimization functionals for the derivation of rectangular parallelopiped element equations. Since the matrix equations include a nonlinear boundary condition linking the free-surface elevation to the interior elements, the Newton-Raphson Method is suggested as a solution method for the governing matrix equations.