| From its birth over20years ago, the lattice Boltzmann method (LBM) has madea more rapid development and at a pace that is strongly accelerating in the past fewyears. The method has found application in different areas of computational fluiddynamics, including simulation of flows in porous media; micro fluid; particulate andsuspension flows. It is different from traditional, LBM has a lot of advantagesincluding a clear physical background, handling simple boundary conditions, easy toimplement. The LBM has been growing concern in worldwide, and application in alot of areas. In recent years, the pattern formation has become a very active area ofresearch, motivated in part by the realization that there are many common aspects ofpatterns formed by diverse physical, chemical, and biological systems and by cellularautomata and differential equation models. The most widely used is Gray-Scott modelin the research of pattern formation.In the article, we simulate the Gray-Scott modelby the lattice Boltzmann method.For LBM, we reviewed the history,basic theory, basic form and current researchof lattice Boltzmann method in the first part of this work, and present derivation oflattice Boltzmann equation(LBE), two-dimension9-velocity model(D2Q9) andboundary conditions. For the Gray-Scott model, we introduce the development,chemical reactions， classification of patterns, reaction-diffusion equations indimensionless in the chapter1and analyzed the linear stability in the chapter2. Thesecond chapter is about the research of Gray-Scott model. Finally, and mostimportantly, we draw the pattern formations of two-dimensional Gray-Scott modelwith different combinations of parameters F and K and different time. In addition, weclassify the different pattern formations. The article compare with the numericalresults with the results obtained by the finite difference scheme. The results show thatthe lattice Boltzmann method can be used to simulate the Gray-Scott model. Thechapter4draws conclusion. |
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