Numerical modeling of turbulent compound channel flow using the lattice Boltzmann method

Abstract

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.

Enhancement of the LABSWE for shallow water flows

“…For instance, in a Godunov-type method, a special treatment for bed slope has to be applied for accurate solutions [8][9][10]; in the lattice Boltzmann method for shallow water equations (LABSWE), the use of the centred scheme for calculation of a bed slope is necessary to produce accurate solutions [7]. As an alternative computational method, the LABSWE has been applied to several complex flow problems, demonstrating its potential, capability and accuracy in simulating shallow water flows [11][12][13]. However, in the LABSWE, the centred scheme involves the determination of the first order derivative associated with a bed slope, which is inconsistent with the spirit of the lattice Boltzmann hydrodynamics.…”

Mixed numerical method for bed evolution

“…In addition, the LBM has been applied successfully to solve the shallow water equations (Dellar, 2002;Li and Huang, 2008;Liu et al, 2009aLiu et al, , 2009bLiu et al, 2010;Peng et al, 2011aPeng et al, , 2011bSalmon, 1999;Zhou, 2004). However, based on the current knowledge, there is no LBM developed for solution of the morphological evolution related to the sediment transport due to the direct inclusion of the empirical estimation of the bed-load transport in the equation.…”

A modified lattice Boltzmann model for shallow water flows over complex topography

“… employed the weighting factor centered scheme for the sourcing term to simulate practical wind‐induced flows in Baiyangdian Lake. In the existing works, for example, , the barotropic term was split into the hydrostatic pressure gradient term and the bed slope term. The hydrostatic pressure gradient term was associated with the quadratic depth term 1/2g h 2 in the equilibrium distribution functions (EDFs), while the bed slope term was treated as an external force and presented as a part of the sourcing term in the lattice Boltzmann equation (LBE).…”