An Improved Hydrodynamic Solution for One-dimensional River Networks and its Applications

Objectives A refined approach is introduced to effectively simulate hydrodynamics in one-dimensional (1D) river networks, enhancing the computational efficiency of the traditional junction water stage iteration method.Methods This approach utilizes the lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model, specifically designed for 1D unsteady open-channel flows. The 1D Saint-Venant equations are solved using the lattice Boltzmann BGK model, where discrete velocity vectors are represented by the D1Q3 model. Equilibrium distribution functions are established to recover the 1D Saint-Venant equations through Chapman-Enskog analysis. The method approximates the spatial derivative of the cross-sectional area in the equilibrium distribution functions using a second-order central difference scheme, achieving an overall second-order spatial accuracy. The coupling of the river network is facilitated through the junction water stage iteration method, initially segmenting the network into various sub-reaches. Water level boundary conditions are imposed at the upper and lower boundaries of each sub-reach. At each time step, the coupling water level is iteratively adjusted to maintain connectivity conditions at all junctions. Given that the lattice Boltzmann BGK model inherently employs an explicit algorithm, it eliminates the necessity for multiple iterations to compute the coupling water level.Results Standard verification scenarios, including steady flows in a looped channel network and unsteady flows in combined looped and treelike networks, were simulated to evaluate the accuracy of the refined method. The hydrodynamics of the middle and lower reaches of the Han River during the autumn flood of 2021 were simulated to validate its utility in real-world applications. The results are as follows:1) For the steady flow scenario in a looped channel network, the simulation outcomes were benchmarked against theoretical analyses, achieving a relative error of up to 7.43%.2) In scenarios involving unsteady flows in combined looped and treelike networks, the refined method precisely simulated the flooding process, with the flood hydrograph’s shape, peak discharge and flood rise and fall times aligning well with prior studies. Various metrics, including total simulation time, total iteration count, average iterations per time step, and average iteration time of the refined method, were compared to those obtained using the traditional junction water stage iteration method and the junctions group method. This comparison revealed that the total and per-step iteration counts of the refined method match those of the traditional method. However, the refined method’s average iteration time was significantly reduced due to eliminating multiple global evolutions per iteration.3) the simulated results were compared to measured data and calculations performed using MIKE software in a real-world case. A remarkable agreement was achieved, with the maximum global relative error of 10⁻²-10⁻³. A comparison of inflow and outflow discharges at a specific river network junction, obtained using the proposed method, the method of characteristics, the Lax diffusive scheme, and the original junction water stage iteration method, revealed that the internal boundary condition of river network junctions cannot be strictly met when employing either the method of characteristics or the Lax diffusive scheme. However, inflow and outflow discharges at river network junctions can be accurately balanced using the proposed method and its original counterpart.Conclusions These findings highlighted the importance, within the context of the junction water stage iteration method, of ensuring that the method utilized to solve the 1D Saint-Venant equations was consistent with that employed to iteratively solve the coupling water level at each river network junction. Although traditional explicit methods, such as the method of characteristics and the Lax diffusive scheme, enhanced computational efficiency by circumventing the global evolution within each iteration, computational accuracy cannot be guaranteed unless a uniform numerical method was employed for the global evolution. The proposed method improved computational efficiency without compromising computational accuracy and ensured that the connection conditions at each river network junction were rigorously maintained.