A Prediction–Correction Solver for Real-Time Simulation of Free-Surface Flows in River Networks

Dechao Hu,Shiming Yao,Shuai Yuan,Yi Liu,Chengkun Duan,Chengwei Lu,Yonghui Zhu

doi:10.3390/w11122525

Abstract

A prediction–correction solver is presented here for rapid simulation of free-surface flows in dendritic and looped river networks. Rather than solving a large global algebraic system over the entire domain of river networks, the model solves subsystems for subdomains of branches in two steps: prediction and correction. With the help of the prediction–correction method (PCM), the partial linearization technique, the semi-implicit method, and the Eulerian–Lagrangian method (ELM), the model only needs to solve tridiagonal linear systems for branches and is free of any iteration. The new model was tested using a hypothetical looped river network with regular cross sections, the Three Gorges Reservoir (TGR) dendritic river network, and the Jing-south looped river system (with seasonally flooding branches). In the first test, a time-step sensitivity study was conducted and the model was revealed to produce accurate simulations at large time steps when the condition for application of the PCM to river networks was satisfied. In the TGR test, the PCM model provided almost the same histories of water levels and discharges as those simulated by the HEC-RAS model. In the Jing-south test, the mean absolute error in simulated water levels was 0.07–0.24 m, and the relative error in simulated cross-section water flux was 0.5–4.9% compared with field data; the conservation error was generally 2 × 10−4 to 3 × 10−4. The PCM model was revealed to be 2–4 times as fast as a reported model, which solves local nonlinear subsystems using two-layer iterations, and 1.2–1.4 times as fast as the HEC-RAS. Using a time step of 1200 s, it took the sequential code 26.8 and 23.1 s to complete a simulation of a one-year unsteady flow process, respectively, in the TGR river networks (with 588 cells) and the Jing-south river system (with 662 cells).

Highlights

In river basin management, rapid decisions are required to cope with emergency events such as dangerous floods, power generation, and so on
In terms of the involved algebraic system, the new model can be differentiated from existing global nonlinear system (GNS), global linear system (GLS), and local nonlinear subsystems (LNS) models and is a fourth kind of river network model: the local linear subsystems (LLS) model
A new model was proposed to simulate free-surface flows in dendritic and looped river networks using the basic idea of the prediction–correction method (PCM)

Summary

Introduction

Rapid decisions are required to cope with emergency events such as dangerous floods, power generation (e.g., short-term regulation), and so on. Simulations of hydrodynamics in river networks are often involved. In short-term power generation scheduling of a large river-type reservoir with many tributaries, the hydrodynamic model is expected to generate results for the optimization model that include influences of dynamic capacities in the upper reaches of reservoirs [1]. The optimization model in this case requires thousands of calls for the hydrodynamic model, and it is expected that the latter can run as fast as possible to provide data for the real-time calls of the former. Flows in all branches of the river networks should be simulated simultaneously to ensure a qualified description of the coupling of the branches. The solution of the coupling of the branches within river networks is often time consuming

Methods

Results

Discussion

Conclusion