Finite element method applied to analysis of flow over a spillway crest

Abstract

SUMMARYNumerical analysis of fluid flow over a spillway is treated in the present paper. A variational principle is introduced for a flow with a free surface boundary under gravity, where the stream function and the profile of the free boundary are independent quantities subjected to variation. A new iteration method is formulated by the combined use of the variational principle and the k i t e element method. A numerical example based on the iterative method is illustrated. Results thus obtained show good agreement with those obtained from an empirical formula.

Numerical Computation of Critical Flow Over a Spillway by Means of Minimization of Violation of Negative Curvature Condition

“…Pausing for a moment, we note that the discretization of problem (6H12) results in an ill-conditioned problem. Indeed, for a sufficiently long upstream region the nowave condition (6) implies that the inlet rin is nearly orthogonal to r&. This together with (9) implies that at the inlet point G, v !…”

Analysis of two-dimensional cavity flow by finite elements

“…The unknown value ~p and ?j of the interior and surthce nodes respectively are detined as generalized coordinates of the nodes. Let ~?~ be the element generalized coordinate vector which is composed of the generalized coordinates of the three nodes of an element e, and R be thr total generalized coordinate vector which is composed of the total n generalized coordinates onthe domain (2 The relation between 1~o and /~ can be expressed as R.,=TeR, ~ = Ta,'/~,…”

“…Luke proved that a variational principle in terms of the velocity potential function can be used for free surface flow. Ikegawa and Washizu [2], Xu TM Table !. Betts I61 had the opinion that in deriving the principle Ikegawa and Washizu incorrectly neglected an integral along the free surface in Green's identity.…”

Types of stationary points in a variational formulation of shallow-water flows

“…The method of classifying relies upon the features of the variable coefficient k(h (x)) in the initial-value problem (10). As observed the main characteristics such as sign and zeros depend on the cubic r(h) (see Fig.…”

“…For the last few years these variational formulations have become an established approach to solving free-surface gravity flows numerically (e.g. [2,3,4,10], [11]). Iterative techniques are invariably used and because of their obvious advantages variants of Newton's Method are widely utilised.…”