BGK Boltzmann Model and Lattice Boltzmann Method for ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

BGK Boltzmann Model and Lattice Boltzmann Method for Shallow Water Flows
Author:Junhong LIANG <celjh@ust.hk> (Department of Civil Engineering, the Hong Kong University of Science and Technology)
Mohamed GHIDAOUI <ghidaoui@ust.hk> (Department of Civil Engineering, the Hong Kong University of Science and Technology)
Presenter:Junhong LIANG <celjh@ust.hk> (Department of Civil Engineering, the Hong Kong University of Science and Technology)
Date: 2006-06-18     Track: Special Sessions     Session: Boltzmann Methods in Water Resources
DOI:10.4122/1.1000000679

Both the Bhatnagar-Gross-Krook (BGK) Boltzmann model and Lattice Boltzmann method (LBM) are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the BGK model. The BGK Boltzmann scheme is a finite volume scheme, where the time-dependent distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. On the other hand, LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. In the field of computational methods for water resources, BGK model is mainly used in shallow water flows and contaminant transport, while application of LBM is focused on low-Froude number shallow water flows, flows in porous media. No existing work has been contributed to compare the performance of both models in the field. In this paper, comparisons for both models are restricted to the shallow water flows. Both BGK and LBM for shallow water equations will be first briefly formulated. Results by both schemes in several benchmark problems in shallow water flows are presented. It is found that the existing LBM model is not suitable for high Froude number flows and fails in the dambreak tests where all three flow regimes, i.e., the supercritical flow, critical flow and subcritical flow coexist, while the BGK model can accurately resolve both bore and rarefaction wave in the test. For low Froude number flows, performances by both models in flows over a hump and Poiseuille flow are comparable.