Lattice Boltzmann method for the Saint–Venant equations

Abstract

The Saint–Venant equations represent the hydrodynamic principles of unsteady flows in open channel network through a set of non-linear partial differential equations. In this paper, a new lattice Boltzmann approach to solving the one-dimensional Saint–Venant equations (LABSVE) is developed, demonstrating the variation of discharge and sectional area with external forces, such as bed slope and bed friction. Our research recovers the Saint–Venant equations through deducing the Chapman–Enskog expansion on the lattice Boltzmann equation, which is a mesoscopic technique, bridging the molecular movement and macroscopic physical variables. It is also a fully explicit process, providing simplicity for programming. The model is verified by three benchmark tests: (i) a one-dimensional subcritical gradient flow; (ii) a dam-break wave flow; (iii) a flood event on the Yongding River. The results showed the accuracy of the proposed method and its good applicability in solving Saint–Venant problems.