A finite element, variable mesh analysis of unconfined steady-state seepage problems is presented based on a nonlinear programming algorithm. It is shown that the minimization of an objective function which merely represents a measure of the total flux leaving or entering the mesh at the free surface nodes (except those that belong also to pervious boundaries) does not permit a unique definition of the free surface geometry. This problem, which is apparently related to the numerical instabilities often met when using variable mesh approaches, can be eliminated by adding to the objective function a term representing a sort of overall regularity condition for the shape of the free surface. The modified solution procedure turns out to be stable and able to provide meaningful results for practical problems even when rather coarse meshes are adopted.
A nonlinear programming analysis of unconfined steady-state seepage
GIODA, GIANCARLO;GENTILE, CARMELO
1987-01-01
Abstract
A finite element, variable mesh analysis of unconfined steady-state seepage problems is presented based on a nonlinear programming algorithm. It is shown that the minimization of an objective function which merely represents a measure of the total flux leaving or entering the mesh at the free surface nodes (except those that belong also to pervious boundaries) does not permit a unique definition of the free surface geometry. This problem, which is apparently related to the numerical instabilities often met when using variable mesh approaches, can be eliminated by adding to the objective function a term representing a sort of overall regularity condition for the shape of the free surface. The modified solution procedure turns out to be stable and able to provide meaningful results for practical problems even when rather coarse meshes are adopted.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
