Presentation on theme: "Artificial Compressibility Method and Lattice Boltzmann Method Similarities and Differences Taku Ohwada ( 大和田 拓） Department of Aeronautics & Astronautics,"— Presentation transcript:
Artificial Compressibility Method and Lattice Boltzmann Method Similarities and Differences Taku Ohwada ( 大和田 拓） Department of Aeronautics & Astronautics, Kyoto University （京都大学大学院工学研究科航空宇宙工学専攻） Collaborators : Prof. Pietro Asinari, Mr. Daisuke Yabusaki May 4, 2011, Spring School on the lattice Boltzmann Method Beijing Computational Science Research Center May 2-6 1 知彼知己者 百戰不殆 If you know your enemies and know yourself, you can win a hundred battles without a single loss
2 0. What is a good numerical method ? Performance Cost (CPU) Education (Human CPU)
21 Considering the fact that the lattice Boltzmann method starts with the kinetic theory and has been derived to conserve high-order isotropy, the lattice Boltzmann method should be more accurate than the artificial compressibility method in capturing pressure waves. He, Doolen, Clark (JCP2002) ACM: Macroscopic (356 papers) LBM: Kinetic (4053 papers)
53 Comparisons of LBM and ACM Taylor-Green Vortex Flow Flow past a Cylinder Lid-driven Cavity Flow Circular Couette Flow ACM is capable of practical 3D simulation Performance of ACM in 3D problems Conclusion LBM – ACM is NOT decisively positive !!! Flow past a Cylinder Lid-driven Cavity Flow
86 Curved Solid Boundary LBM ACM: Macroscopic data Interpolation or extrapolation e.g. Interpolation Bounce-Back Bouzidi, Firdaouss, Lallemand (2001) Ginzburg, d’Humières (2003)
87 x N W S E P y B Solid Body Fluid W E P B Quadratic extrapolation x at B
88 x N W S E P y B Solid Body Fluid W E P B Quadratic extrapolation x at B at P
Why not ACM? 89 Since the ACM does not employ any kinetic theory gadget, it is much easier than the LBM. Up to now, any decisive inferiority of ACM to LBM has not been found. Conversely, superiority of ACM over LBM has been found in some fundamental test problems. Therefore, it is highly recommended to master ACM before learning LBM.
Richardson extrapolation = 累遍増約術 Its usefulness for practical computations can hardly be overestimated. Birkoff & Rota, Ordinary differential equations (1978). Lewis Fry Richardson, ``Approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam ‘’, Phil. Trans. Royal Soc. London, Series A 210: 307–357 (1910).