Using a characteristic-based particle tracking method to solve one-dimensional fully dynamic wave flow

Abstract

The theoretical behavior of a one-dimensional (1-D) open-channel flow is embedded in the Saint-Venant equation, which is derived from the Navier–Stokes equations. The flow motion is described by the momentum equations, in which the terms for the inertia, pressure, gravity, and friction loss are retained while all other terms are discarded. Although the problem is valid for most channel-flow scenarios, it is numerically challenging to solve because robust, accurate, and efficient algorithms are critical for models to field applications. The method of characteristics (MOC) is applied to solve the diagonalized Saint-Venant equations. Most importantly, the boundary conditions can be naturally implemented based on the wave directions. This is considered more closely related to realistic flow conditions and sufficiently flexible to handle mixed sub- and supercritical fluid flows in natural rivers. A computer model, WASH1DF, derived from the proposed numerical method, and which differs from other commercial software packages such as HEC-RAS and SOBEK, was developed. To test the accuracy of the proposed method, four benchmark problems were examined. Analytical solutions to these benchmark problems, covering a wide range of cases, were provided by MacDonald et al. (J. Hydrol. Eng. ASCE 123(11), 1041–1045, 1997). The simulations indicate that the proposed method provides accurate results for all benchmark cases, which are valid for all transient flow scenarios. Comparisons of WASH1DF with other commercially available software packages were also conducted under the same simulation conditions. The results indicate that our proposed model demonstrates high accuracy for all problems and achieves the highest simulation precision among all packages tested.