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  • 學位論文

晶格波茲曼法邊界條件之發展

Development of boundary condition in lattice Boltzmann method

指導教授 : 林昭安

摘要


In the thesis, a lattice Boltzmann boundary treatment for pressure and velocity boundary conditions is presented. A new boundary condition is proposed to handle the unknown distribution functions at the boundaries. We assume every unknown distribution function has a correction term F for modification. The singular corner point is treated by two types of methods, and obtain a close result. This scheme is applied to two-dimensional Poiseuille flow, Couette flow with wall injection, lid-driven square cavity flow, and three-dimensional Poiseuille flow. Numerical simulations exhibit the scheme is second order accurate in space discretization.

並列摘要


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參考文獻


[1] X. Shan and H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components," Phys. Rev. E 47, 1815, 1993.
[2] X. Shan and H. Chen, Simulation of non-ideal gases and liquid-gas phase transition by the lattice Boltzmann equation," Phys. Rev. E 49, 2941, 1994.
[3] A. J. C. Ladd, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part I. Theoretical foundation," J. Fluid Mech. 271, 285, 1994;
[4] A. J. C. Ladd, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part II. Numerical results," J. Fluid Mech. 271, 311, 1994.
[6] S. P. Dawson, S. Chen and G. Doolen, Lattice Boltzmann computations for reactiondi®usion equations," J. Comp. Phys. 98, 1514, 1993.

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