Abstract
Simulating shallow water flows in large scale river-lake systems is important but challenging because huge computer resources and time are needed. This paper aimed to propose a simple and efficient 1D–2D coupled model for simulating these flows. The newly developed lattice Boltzmann (LB) method was adopted to simulate 1D and 2D flows, because of its easy implementation, intrinsic parallelism, and high accuracy. The coupling strategy of the 1D–2D interfaces was implemented at the mesoscopic level, in which the unknown distribution functions at the coupling interfaces were calculated by the known distribution functions and the primitive variables from the adjacent 1D and 2D lattice nodes. To verify the numerical accuracy and stability, numerical tests, including dam-break flow and surge waves in the tailrace canal of a hydropower station, were simulated by the proposed model. The results agreed well with both analytical solutions and commercial software results, and second-order convergence was verified. The application of the proposed model in simulating the surge wave propagation and reflection phenomena in a reservoir of a run-of-river hydropower station indicated that it had a huge advantage in simulating flows in large-scale river-lake systems.
Highlights
One-dimensional (1D) and two-dimensional (2D) shallow water equations are widely used to simulate flows in rivers, lakes, reservoirs, and estuaries
This paper aimed to propose a 1D–2D coupled model for simulating shallow water flows in river-lake systems
A 1D–2D coupled model was developed for shallow water simulations in large scale river-lake systems, in which both 1D and 2D submodels were numerically solved by the lattice Boltzmann (LB) method
Summary
One-dimensional (1D) and two-dimensional (2D) shallow water equations are widely used to simulate flows in rivers, lakes, reservoirs, and estuaries. The cross-sectional integrated 1D models are extremely suitable for hydrodynamic simulations in large scale river networks, with their lumped boundary representations for hydraulic structures, such as weirs, dams, culverts, and pumps. 2D models, with their ability to accurately resolve flows in both longitudinal and transversal directions, are the primary choice for hydrodynamic simulations for lakes, reservoirs, and estuaries. The numerical solvers for the shallow water equations are mainly based on traditional methods, such as an implicit finite-difference scheme for the 1D model and finite-volume method for the 2D model [1,2,3]. Even if being accepted widely, these traditional methods are relatively difficult to
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