Lattice Boltzmann method for the Saint-Venant equations

- We develop a LABSVE model using lattice Boltzmann method.
- The model is a new approach to solving the one-dimensional Saint-Venant equations.
- The solution is proved through deducing the Chapman-Enskog expansion.
- The model is able to simulate steep water front.
- The model is applied to a flood event on the Yongding River.

SummaryThe 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.