A BGK MODEL FOR THREE-DIMENSIONAL SHALLOW WATER PROBLEMS

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

A BGK MODEL FOR THREE-DIMENSIONAL SHALLOW WATER PROBLEMS
Paper
Author:Mohamed S. Ghidaoui <ghidaoui@ust.hk> (Dept of Civil Engineering, The Hong Kong University of Science & Technology)
Jun Hong Liang <celjh@ust.hk> (Dept of Civil Engineering, The Hong Kong University of Science & Technology)
Presenter:Mohamed S. Ghidaoui <ghidaoui@ust.hk> (Dept of Civil Engineering, The Hong Kong University of Science & Technology)
Date: 2006-06-18     Track: Special Sessions     Session: Boltzmann Methods in Water Resources
DOI:10.4122/1.1000000501
DOI:10.4122/1.1000000502

This paper focuses on illustrating how the Boltzmann theory can be used to formulate numerical algorithms for three-dimensional shallow water equations. The paper begins by showing that the classical three-dimensional shallow water equations are obtainable from the moments of the Boltzmann Bhatnagar-Gross-Krook (BGK) equation. This connection is then exploited to formulate a three-dimensional finite volume for shallow flows in which the fluxes are obtained on the basis of the BGK equation. The resulting scheme is illustrated using a variety of surface water problems. The advantages of using the Boltzmann-based to formulate numerical algorithms for surface water flows are summarized.