Viscosity-excluded formulations of 2-D river flow with a new wetting and drying algorithm

Abstract

An efficient method for simulating 2-D river flow is developed in which horizontal turbulent shears are omitted from the 2-D depth-averaged momentum equations. It is shown that a pseudo-viscosity can be reproduced to take into account the lost shear action, by incorporating the vertically integrated continuity equation to the momentum equations and transforming the latter into a discrete integral form. To simulate river flows with wet and dry areas, negative water depths are allowed when solving the continuity equation. The concept of negative water depth enables us to track flow boundaries with about the same accuracy but much less effort as compared with traditional numerical methods. An optimal threshold value defining dry areas is first obtained by one-dimensional theoretical analysis and then sought by trial-and-error for two-dimensional flow simulation with tolerable node-to-node spurious oscillations, while mass is best conserved. Numerical solutions using the new procedure are compared with the one-dimensional benchmark solution of the Saint Venant equations and the experimental data from a two-stage channel. Robustness of the present approach is also tested through the study of water flow in a natural river and a hypothetical channel with several bumps.