A dissipative finite element model for discontinuous unsteady flow in open channel

Abstract

The purpose of this paper is to present a dissipative finite-element formulation applicable to discontinuous one-dimensional open-channel flow. The traditional Galerkin approximation seems to be inappropriate for simulation of open-channel flow when discontinuities are introduced in the flow domain; the solutions show undesirable oscillations in the vicinity of the discontinuity. The method presented herein is a weighted residual formulation based on discontinuous weighting functions which are not identical to the shape functions; it provides smoother and more accurate results than the standard Galerkin approximation, offering to the finite-element method the ability of simulating steep wave fronts. The dissipative model is applied to flow with surges in a rectangular horizontal channel. Computational results are compared with experimental data and with results obtained by finite-difference schemes.