求解复杂边界的直接力浸入边界-格子Boltzmann耦合方法
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摘要
本文对直接力浸入边界-格子Boltzmann耦合方法中两种常用LB方程中引入外力项的方法(EBF和GZS模型)以及基于压力的He-Luo模型与基于密度的LBGK模型两种LB方程的方法分别进行了对比分析.结果表明对于不可压流动,GZS模型精度比EBF模型高,而He-Luo模型精度与比标准LBGK模型高.采用多重力法可有效减小直接力IB方法会出现的边界无滑移条件误差,发现数值边界相对物理边界产生外扩现象,通过边界内缩方法可以使得数值边界与物理边界重合,实现边界的真正无滑移条件.
Two common schemes(EBF and GZS method) introducing external force term into LB equations in direct forcing immersed boundary-lattice Boltzmann method coupling method are analyzed comparatively. Meanwhile, two common LB models are considered which one is He-Luo equation based on pressure and the other is standard LBGK equation based on density. The results show that for incompressible flow, GZS scheme and He-Luo model is more accurate than EBF scheme and LBGK model, respectively. And the error of boundary non-slip condition can be reduced effectively by multi-direct forcing strategy. Furthermore, a phenomenon that numerical boundary slightly expanded from physical boundary is intuitively found. It can be effectively corrected and hence the non-slip condition can be sufficiently satisfied by further slightly retracting the numerical boundary to coincide with the physical boundary.
Two common schemes(EBF and GZS method) introducing external force term into LB equations in direct forcing immersed boundary-lattice Boltzmann method coupling method are analyzed comparatively. Meanwhile, two common LB models are considered which one is He-Luo equation based on pressure and the other is standard LBGK equation based on density. The results show that for incompressible flow, GZS scheme and He-Luo model is more accurate than EBF scheme and LBGK model, respectively. And the error of boundary non-slip condition can be reduced effectively by multi-direct forcing strategy. Furthermore, a phenomenon that numerical boundary slightly expanded from physical boundary is intuitively found. It can be effectively corrected and hence the non-slip condition can be sufficiently satisfied by further slightly retracting the numerical boundary to coincide with the physical boundary.
引文
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[14] Uhlmann M. An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows[J].Journal of Computational Physics, 2005, 209(2):448-476
[15] Su S W, Lai M C, Lin C A. An Immersed Boundary Technique for Simulating Complex Flows with Rigid Boundary[J]. Computers&Fluids, 2007, 36(2):313-324
[16] Silva A L F L E, Silveira-Neto A, Damasceno J J R. Numerical Simulation of Two-dimensional Flows Over a Circular Cylinder Using the Immersed Boundary Method[J].Journal of Computational Physics, 2003, 189(2):351-370
[17] Feng Z G, Michaelides E E. Robust Treatment of Noslip Boundary Condition and Velocity Updating for the Lattice-Boltzmann Simulation of Particulate flows[J].Computers&Fluids, 2009, 38(2):370-381
[2] Mittal R, Iaccarino G. Immersed Boundary Method[J].Annual Review of Fluid Mechanics, 2005, 14(37):239-261
[3] Feng Z G, Michaelides E E. Proteus:a Direct Forcing Method in the Simulations of Particulate Flows[J]. Journal of Computational Physics, 2005, 202(1):20-51
[4] Wu J, Aidun C K. Simulating 3D Deformable particle Suspensions Using Lattice Boltzmann Method with Discrete External Boundary Force[J]. International Journalfor Numerical Methods in Fluids, 2010, 62(7):765-783
[5] Dupuis A, Chatelain P, Koumoutsakos P. An Immersed Boundary-Lattice-Boltzmann Method for the Simulation of the Flow Past an Impulsively Started Cylinder[J]. Journal of Computational Physics, 2008, 227(9):4486-4498
[6] Guo Z, Zheng C, Shi B. Discrete Lattice Effects on the forcing Term in the Lattice Boltzmann Method[J]. Physical Review E, 2002, 65(4):046308(1-6)
[7] Kang S K. Immersed Boundary Methods in the Lattice Boltzmann Equation for flow Simulation[M]. Texas A&M University, 2010
[8] Kang S K, Hassan Y A. A Comparative Study of Directforcing Immersed Boundary-lattice Boltzmann Methods for Stationary Complex Boundaries[J]. International Journal for Numerical Methods in Fluids, 2011, 66(9):1132-1158
[9] Eshghinejadfard A, Abdelsamie A, Janiga G, et al. Directforcing Immersed Boundary Lattice Boltzmann Simulation of Particle/fluid Interactions for Spherical and Nonspherical Particles[J]. Particuology, 2016, 25(2):93-103
[10] Shan X, Chen H. Lattice Boltzmann Model for Simulating Flows With Multiple Phases and Components[J]. Physical Review E, 1993, 47(3):1815-1819
[11] He X, Luo L S. Theory of the Lattice Boltzmann Method:From the Boltzmann Equation to the Lattice Boltzmann Equation[J]. Physical Review E, 1997, 56(6):6811-6817
[12] Luo K, Wang Z,Fan J,et al. Full-scale Solutions to Particle-laden Flows:Multidirect Forcing and Immersed Boundary Method[J]. Physical Review E, 2007, 76(6):066709(1-9)
[13] Wang Z, Fan J, Luo K. Combined Multi-direct Forcing and Immersed Boundary Method for Simulating Flows with Moving Particles[J]. International Journal of Multiphase Flow, 2008, 34(3):283-302
[14] Uhlmann M. An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows[J].Journal of Computational Physics, 2005, 209(2):448-476
[15] Su S W, Lai M C, Lin C A. An Immersed Boundary Technique for Simulating Complex Flows with Rigid Boundary[J]. Computers&Fluids, 2007, 36(2):313-324
[16] Silva A L F L E, Silveira-Neto A, Damasceno J J R. Numerical Simulation of Two-dimensional Flows Over a Circular Cylinder Using the Immersed Boundary Method[J].Journal of Computational Physics, 2003, 189(2):351-370
[17] Feng Z G, Michaelides E E. Robust Treatment of Noslip Boundary Condition and Velocity Updating for the Lattice-Boltzmann Simulation of Particulate flows[J].Computers&Fluids, 2009, 38(2):370-381