Asymmetric lattice Boltzmann model for shallow water flows

Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

Download Full-text

A 1D–2D Coupled Lattice Boltzmann Model for Shallow Water Flows in Large Scale River-Lake Systems

Applied Sciences ◽

10.3390/app10010108 ◽

2019 ◽

Vol 10 (1) ◽

pp. 108

Author(s):

Wanwan Meng ◽

Yongguang Cheng ◽

Jiayang Wu ◽

Chunze Zhang ◽

Linsheng Xia

Keyword(s):

Shallow Water ◽

Lattice Boltzmann ◽

Large Scale ◽

Distribution Functions ◽

Lattice Boltzmann Model ◽

Hydropower Station ◽

Water Flows ◽

Shallow Water Flows ◽

Proposed Model ◽

Lake Systems

Simulating shallow water flows in large scale river-lake systems is important but challenging because huge computer resources and time are needed. This paper aimed to propose a simple and efficient 1D–2D coupled model for simulating these flows. The newly developed lattice Boltzmann (LB) method was adopted to simulate 1D and 2D flows, because of its easy implementation, intrinsic parallelism, and high accuracy. The coupling strategy of the 1D–2D interfaces was implemented at the mesoscopic level, in which the unknown distribution functions at the coupling interfaces were calculated by the known distribution functions and the primitive variables from the adjacent 1D and 2D lattice nodes. To verify the numerical accuracy and stability, numerical tests, including dam-break flow and surge waves in the tailrace canal of a hydropower station, were simulated by the proposed model. The results agreed well with both analytical solutions and commercial software results, and second-order convergence was verified. The application of the proposed model in simulating the surge wave propagation and reflection phenomena in a reservoir of a run-of-river hydropower station indicated that it had a huge advantage in simulating flows in large-scale river-lake systems.

Download Full-text

LATTICE BOLTZMANN SIMULATIONS OF DISCONTINUOUS FLOWS

International Journal of Modern Physics C ◽

10.1142/s0129183107010280 ◽

2007 ◽

Vol 18 (01) ◽

pp. 1-14 ◽

Cited By ~ 10

Author(s):

JIAN GUO ZHOU

Keyword(s):

Shallow Water ◽

Lattice Boltzmann ◽

Wave Interaction ◽

Elastic Collision ◽

Lattice Boltzmann Model ◽

Curved Boundaries ◽

Slip Boundary ◽

Lattice Boltzmann Simulations ◽

Shallow Water Flows ◽

Boltzmann Model

The lattice Boltzmann model for the shallow water equations (LABSWE) is applied to the simulation of certain discontinuous flows. Curved boundaries are treated efficiently, using either the elastic-collision scheme for slip and semi-slip boundary conditions or the bounce-back scheme for no-slip conditions. The force term is accurately determined by means of the centred scheme. Simulations are presented of a small pulse-like perturbation of the still water surface, a dam break, and a surge wave interaction with a circular cylinder. The results agree well with predictions from alternative high-resolution Riemann solver based methods, demonstrating the capability of LABSWE to predict shallow water flows containing discontinuities.

Download Full-text

MODELING MOVING BOUNDARY IN SHALLOW WATER BY LBM

International Journal of Modern Physics C ◽

10.1142/s0129183112500945 ◽

2013 ◽

Vol 24 (01) ◽

pp. 1250094 ◽

Cited By ~ 3

Author(s):

Y. PENG ◽

J. G. ZHOU ◽

J. M. ZHANG ◽

R. BURROWS

Keyword(s):

Shallow Water ◽

Present Model ◽

Moving Boundary ◽

Lattice Boltzmann Model ◽

Shallow Waters ◽

Shallow Water Flows ◽

Moving Body ◽

Body Boundary ◽

Multiple Relaxation Time ◽

Boltzmann Model

A lattice Boltzmann model (LBM) for a moving body in shallow waters is developed. Three different schemes, FH's, Guo's and MMP's schemes, for a curved boundary condition at second-order accuracy are used in the study and compared in detail. The multiple-relaxation-time (MRT) is adopted for better stability. In order to deal with the moving body boundary, a certain momentum is added to reflect the interaction between the fluid and the solid; and a refill method for new wetted nodes moving out from solid nodes has been proposed. The described method is applied to simulate static and moving cylinders in shallow waters. The corresponding experiments are further performed for validation of the present model. It is found that all of the three schemes produce similar results that agree well with the experimental data for the static cylinder. However, for the moving boundary, MMP's scheme performs best. Overall, the proposed modeling approach is able to simulate both, static and moving cylinders in shallow water flows at acceptable accuracy.

Download Full-text