Development of physically based meshes for two-dimensional models of meandering channel flow

Abstract

The choice of mesh generation and numerical solution strategies for two-dimensional finite element models of fluvial flow have previously been based chiefly on experience and rule of thumb. This paper develops a rationale for the finite element modelling of flow in river channels, based on a study of flow around an annular reach. Analytical solutions of the two-dimensional Shallow Water (St. Venant) equations are developed in plane polar co-ordinates, and a comparison with results obtained from the TELEMAC-2-D finite element model indicates that of the two numerical schemes for the advection terms tested, a flux conservative transport scheme gives better results than a streamline upwind Petrov–Galerkin technique. In terms of mesh discretization, the element angular deviation is found to be the most significant control on the accuracy of the finite element solutions. A structured channel mesh generator is therefore developed which takes local channel curvature into account in the meshing process. Results indicate that simulations using curvature-dependent meshes offer similar levels of accuracy to finer meshes made up of elements of uniform length, with the added advantage of improved model mass conservation in regions of high channel curvature. Copyright © 2000 John Wiley & Sons, Ltd.