Abstract
A sub-grid multiple relaxation time (MRT) lattice Boltzmann model with curvilinear coordinates is applied to simulate an artificial meandering river. The method is based on the D2Q9 model and standard Smagorinsky sub-grid scale (SGS) model is introduced to simulate meandering flows. The interpolation supplemented lattice Boltzmann method (ISLBM) and the non-equilibrium extrapolation method are used for second-order accuracy and boundary conditions. The proposed model was validated by a meandering channel with a 180° bend and applied to a steady curved river with piers. Excellent agreement between the simulated results and previous computational and experimental data was found, showing that MRT-LBM (MRT lattice Boltzmann method) coupled with a Smagorinsky sub-grid scale (SGS) model in a curvilinear coordinates grid is capable of simulating practical meandering flows.
Highlights
Derived from the Lattice Gas Automata (LGA) [1,2], the single relaxation method (called the latticeBhatnagar Gross Krook (LBGK) method) [3,4] is a promising and powerful tool for computational fluid dynamics
The multiple relaxation time (MRT) lattice Boltzmann method was proposed and developed [13,14,15] to overcome these shortcomings; by establishing a model on moment space rather than on discrete space, different relaxation times can be chosen for different moments, which leads to an improvement in the stability of the LBGK method [15]
Zhao applied the GILBM to shallow water equations, allowing the flow problem in curved and meandering open channels to be accurately resolved based on a curvilinear coordinate grid system [26]
Summary
Derived from the Lattice Gas Automata (LGA) [1,2], the single relaxation method Different methods have been developed to extend the LBM on a nonuniform mesh, including the interpolation-supplemented scheme (ISLBE) [16], grid refinement scheme [17,18,19], dynamically adaptive grids for shallow water simulations [20], and the MRT-LBM for transformed equations in a curvilinear coordinates system [21]. Zhao applied the GILBM to shallow water equations, allowing the flow problem in curved and meandering open channels to be accurately resolved based on a curvilinear coordinate grid system [26].
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