Abstract
A new lattice Boltzmann method to simulate open channel flows with complex geometry described by a conservative form of Saint-Venant equations is developed. The Saint-Venant equations include an original treatment of the momentum equation source term. Concrete hydrostatic pressure thrust expressions are provided for rectangular, trapezoidal and irregular cross-section shapes. A D1Q3 lattice arrangement is adopted. External forces, such as bed friction and the static term, are discretized with a centred scheme. Bounce back and imposed boundary conditions are considered. To verify the proposed model, four cases are carried out: tidal flow over a regular bed in a rectangular cross-section, steady flow in a channel with horizontal and vertical contractions, steady flow over a bump in a trapezoidal channel and steady flow in a non-prismatic channel with friction. Results indicate that the proposed scheme is simple and can provide accurate predictions for open channel flows.
Highlights
Numerical modelling of one-dimensional (1D) open channel flows described by a conservative form of Saint-Venant equations [1,2,3,4] is a central topic in hydraulic and hydrologic research
Chang et al [7] presented a mesh-less numerical model based on smoothed particle hydrodynamics to simulate 1D open channel flows
In the area of simulating the open channel flows described by Saint-Venant equations, the lattice Boltzmann (LB) method is suitable for subcritical flows, which are the most common scenarios in coastal areas, estuaries and rivers
Summary
Numerical modelling of one-dimensional (1D) open channel flows described by a conservative form of Saint-Venant equations [1,2,3,4] is a central topic in hydraulic and hydrologic research. In the area of simulating the open channel flows described by Saint-Venant equations, the LB method is suitable for subcritical flows, which are the most common scenarios in coastal areas, estuaries and rivers. It suffers from a numerical instability when the LB method is used to solve the supercritical flows. Liu et al [20] proposed an LB model to solve the 1D non-conservative form of Saint-Venant equations under the assumption that the width change of river cross-sections is inconspicuous along the stream-wise direction.
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