Solute transport in shallow water flows using the coupled curvilinear Lattice Boltzmann method

The coupled lattice Boltzmann method (CLBM) is applied in investigating contamination transport in shallow water flows. Shallow water equations and advection-diffusion equation are both solved using lattice Boltzmann method (LBM) on a D2Q9 square lattice and Bhatnagar-Gross-Krook (BGK) term. For extending application of CLBM in shallow water flows, the well-balanced scheme is introduced to replace the source term. Three cases including dam break, 2D pure diffusion and complex tidal flow are calculated and analyzed. Dam break and 2D pure diffusion are prepared to validate the flow module and water quality module, respectively. Both the cases show satisfactory consistency between predicting results and analytical solutions. Since clear reproduction of the shock wave propagation and precise prediction of contamination transport are derived, LBM is proved to be the numerical method naturally conservative with acceptable computing error. Furthermore, complex tidal flow with irregular geometry and sinus-varied bathymetry is simulated by adopting the well-balanced treating on the source term. The velocity fields, water levels, and water quality are compared between the ebb tide and flood tide, the results of which are in excellent accordance with the physical laws during the process. Hence, it may demonstrate that improved by well-balanced scheme CLBM can be widely applicable in shallow water flow.

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Simulation of Sound Emitted from Collision of Droplet with Shallow Water by the Lattice Boltzmann Method

Computational Science – ICCS 2008 - Lecture Notes in Computer Science ◽

10.1007/978-3-540-69387-1_30 ◽

2008 ◽

pp. 271-280 ◽

Cited By ~ 1

Author(s):

Shinsuke Tajiri ◽

Michihisa Tsutahara ◽

Hisao Tanaka

Keyword(s):

Lattice Boltzmann Method ◽

Shallow Water ◽

Lattice Boltzmann ◽

Boltzmann Method

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Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

Mathematical Problems in Engineering ◽

10.1155/2017/8917360 ◽

2017 ◽

Vol 2017 ◽

pp. 1-5 ◽

Cited By ~ 2

Author(s):

Y. Peng ◽

J. P. Meng ◽

J. M. Zhang

Keyword(s):

Shallow Water ◽

Lattice Boltzmann ◽

Lattice Models ◽

Second Order ◽

Lattice Boltzmann Model ◽

Space Filling ◽

Order Accuracy ◽

Water Flows ◽

Recent Success ◽

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.

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