Lattice Boltzmann modeling of shallow water flows over discontinuous beds |
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Authors: | Y. Peng J. G. Zhou J. M. Zhang H. Liu |
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Affiliation: | 1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, China;2. School of Engineering, University of Liverpool, Liverpool, UK;3. School of Environment, Beijing Normal University, Beijing, China |
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Abstract: | Numerical 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. |
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Keywords: | shallow water flows Lattice Boltzmann model discontinuous bed, force term centered scheme LABSWEBGK LABSWEMRT |
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