A Simple and Efficient Method with Godunov-Type Schemes for Flow Simulation at Junctions of Open Channel Networks

Abstract

This paper presents a numerical model for simulating flows in open channel networks by discretizing the Saint-Venant equations via a Godunov-type scheme. The methodology integrates the Harten Lax van Leer (HLL) approximate Riemann solution scheme for interface flux, the slope flux method for water surface slope terms, and an explicit method for handling friction source terms. A novel aspect of this work is the introduction of the artificial area method to treat junction points as nodes with fixed, constant areas, thus eliminating the need for iterative computations. A generalized approach is proposed to calculate these fixed areas on the basis of the characteristics of adjacent river nodes. Additionally, two other junction calculation methods—the method of characteristics and the Riemann iteration method—are developed to assess the effectiveness of the artificial area method. The performance of various junction models is evaluated via simulations with three independent channels and three channel networks. The results show a high degree of consistency among the simulated outcomes, exact solutions, experimental measurements, and findings from the literature. Furthermore, the artificial area method demonstrates significant agreement with the other junction methods. Notably, the artificial area method significantly enhances computational efficiency at junction points, achieving speed improvements ranging from 30 to 290 times faster than those of the other two methods. In conclusion, the artificial area method is characterized by its simplicity, effectiveness, and ease of implementation. Its computational accuracy is on par with that of other methods, rendering it widely applicable for simulating flows in open channel networks. This work contributes valuable insights into numerical modeling techniques for hydraulic engineering applications.