Premium
An evaluation of force terms in the lattice Boltzmann models in simulating shallow water flows over complex topography
Author(s) -
Li Shaotian,
Li Yineng,
Zeng Zeyu,
Huang Ping,
Peng Shiqiu
Publication year - 2019
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4726
Subject(s) - lattice boltzmann methods , forcing (mathematics) , waves and shallow water , weighting , quadratic equation , shallow water equations , mechanics , flow (mathematics) , momentum (technical analysis) , geology , mathematics , physics , geometry , mathematical analysis , oceanography , finance , acoustics , economics
Summary Proper approximation of the force terms, especially the bed slope term, is of crucial importance to simulating shallow water flows in lattice Boltzmann (LB) models. However, there is little discussion on the schemes of adding force terms to LB models for shallow water equations (SWEs). In this study, we evaluate the performance of forcing schemes coupled with different LB models (LABSWE and MLBSWE) in simulating shallow water flows over complex topography and try to find out their intrinsic characteristics and applicability. Three cases are adopted for evaluation, including a stationary case, a one‐dimensional tidal wave flow over an irregular bed, and a steady flow over a two‐dimensional seamount. The simulating results are compared with analytical solutions or the results produced by the finite difference method. For LABSWE, all the forcing schemes, except for the weighting factor method, fail to produce accurate solutions for the test cases; this is probably due to the mismatch between the bed slope term in source terms and the quadratic depth term of the equilibrium distribution functions in these forcing schemes. For MLBSWE, all the forcing schemes are capable of simulating flows over the complex topography accurately; furthermore, those schemes taking into account the collision effect τ to eliminate the momentum induced by forces provide more accurate solutions with quicker convergence as the lattice size decreases. In this view, MLBSWE can bring more flexibility in treating the force terms and thus can be a better tool to simulate shallow water flows over complex topography in practical application.