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SUMMARYThe flow of water in a straight compound channel with prismatic cross section is investigated with a relatively new tool, the lattice Boltzmann method. The large eddy simulation model is added in the lattice Boltzmann model for nonlinear shallow water equations (LABSWE TM ) so that the turbulence, caused by lateral exchange of momentum in the shear layer between the main channel and floodplain, can be taken into account and modeled efficiently. To validate the numerical model, a symmetrical compound channel with trapezoidal main channel and flat floodplain is tested. Similar to most natural watercourses, the floodplain has higher roughness values than the main channel. Different relative depths, D r (the ratio of the depth of flow on the floodplain to that in the main channel), are considered. The Reynolds number is set at 30 000 in the main channel. The lateral distributions of the longitudinal velocity, the boundary shear stress, the Reynolds stress and the apparent shear stress across the channel are obtained after the large eddy simulation is performed. The results of numerical simulations are compared with the available experiment data, which show that the LABSWE TM is capable of modeling the features of flow turbulence in compound channels and is sufficiently accurate for practical applications in engineering.

The paper reports a new lattice Boltzmann approach to simulating wetting-drying processes in shallow-water flows. The scheme is developed based on the ChapmanEnskog analysis and the Taylor expansion, which is consistent with the theory of the lattice Boltzmann method. All the forces, such as bed slope and bed friction, are taken into account naturally in determining the wet-dry interface, without the use of either the spurious assumption of a thin water film on a dry bed or the non-physical extrapolation of certain variables such as water depth or velocity. This offers a simple and general model for simulating wetting-drying processes in complex flows involving external forces. Its verification is carried out by modelling several one-dimensional (1D) and two-dimensional (2D) flows: (i) 1D sloshing over a parabolic container; (ii) a 1D tidal wave over three adverse bed slopes; (iii) a 1D solitary wave run up on a plane sloping beach; (iv) a tsunami run up on a plane beach; (v) a 2D stationary case with wet-dry boundaries; (vi) a 2D long-wave resonance over a parabolic basin; and (vii) a 2D solitary wave run up on a conical island. The numerical results agree well with analytical solutions, other numerical results and experimental data, demonstrating the effectiveness and accuracy of the new approach.

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SUMMARYNumerical modeling of shallow water flows over discontinuous beds is presented. The flows are described with the shallow water equations and the equations are solved using the lattice Boltzmann method (LBM) with single relaxation time (Bhatnagar–Gross–Krook‐LBM (BGK‐LBM)) and the multiple relaxation time (MRT‐LBM). The weighted centered scheme for force term together with the bed height for a bed slope is described to improve simulation of flows over discontinuous bed. Furthermore, the resistance stress is added to include the local head loss caused by flow over a step. Four test cases, one‐dimensional tidal over regular bed and steps, dam‐break flows, and two‐dimensional shallow water flow over a square block, are considered to verify the present method. Agreements between predictions and analytical solutions are satisfactory. Furthermore, the performance and CPU cost time of BGK‐LBM and MRT‐LBM are compared and studied. The results have shown that the lattice Boltzmann method is simple and accurate for simulating shallow water flows over discontinuous beds. This demonstrates the capability and applicability of the lattice Boltzmann method in modeling shallow water flows on bed topography with a discontinuity in practical hydraulic engineering. Copyright © 2014 John Wiley & Sons, Ltd.