A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of t...A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.展开更多
A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow.The computational efficiency and accuracy are both enhanced....A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow.The computational efficiency and accuracy are both enhanced.The restriction to the relaxation factor （which needs to be smaller than 1） is circumvented by the new surface tension algebra,due to its rational physical nature compared with the treatment of Xing,Buther and Yang in their paper （Comp.Mater.Sci.,2007,39（2）：282-290）.The proposed stable surface tension scheme is applied to simulate the free deformation of a square droplet with surface tension effect and the process of a droplet impinging on a liquid film.The numerical solution for free deformation of a droplet agrees well with thermodynamic principles,and also achieves high accuracy in comparison with Xing,et al.＇s model.Three typical impinging modes are successfully obtained with the new scheme,and another particular mode found by Wang and Chen is also successfully simulated.The evolutions of liquid crown agree well with the power law related to time.展开更多
The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is ...The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is found that the flux of the enstrophy cascades to small scales and the direction cascade of the energy flux is upscaled. Moveover, the probability distribution function （PDF） of the enstrophy flux gives a clear evidence that the enstrophy cascades to smaller scales. Finally, the behavior of the cascade of the high-order Casimir invariants Zn is discussed. The flux of the fourth-order Casimir invariant Z4 cascades to small scales. The flux of Zn has a logarithmic relationship with the scale, that is,∏ 1^zn - l^ζn （n = 2,4,6）.展开更多
文摘A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.
基金supported by the National Natural Science Foundation of China (Grant Nos.10625210,50609020 and 10902070)the Leading Academic Discipline Project of Shanghai Municipal Education Commission (Grant No.J50501)
文摘A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow.The computational efficiency and accuracy are both enhanced.The restriction to the relaxation factor （which needs to be smaller than 1） is circumvented by the new surface tension algebra,due to its rational physical nature compared with the treatment of Xing,Buther and Yang in their paper （Comp.Mater.Sci.,2007,39（2）：282-290）.The proposed stable surface tension scheme is applied to simulate the free deformation of a square droplet with surface tension effect and the process of a droplet impinging on a liquid film.The numerical solution for free deformation of a droplet agrees well with thermodynamic principles,and also achieves high accuracy in comparison with Xing,et al.＇s model.Three typical impinging modes are successfully obtained with the new scheme,and another particular mode found by Wang and Chen is also successfully simulated.The evolutions of liquid crown agree well with the power law related to time.
基金supported by the National Natural Science Foundation of China(Grant No.91441104)the Ministry of Education in China via project(Grant No.IRT0844)the Shanghai Science and Technology Commission Project of leading Scientists and Excellent Academic Leaders(Grant No.11XD1402300)
文摘The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is found that the flux of the enstrophy cascades to small scales and the direction cascade of the energy flux is upscaled. Moveover, the probability distribution function （PDF） of the enstrophy flux gives a clear evidence that the enstrophy cascades to smaller scales. Finally, the behavior of the cascade of the high-order Casimir invariants Zn is discussed. The flux of the fourth-order Casimir invariant Z4 cascades to small scales. The flux of Zn has a logarithmic relationship with the scale, that is,∏ 1^zn - l^ζn （n = 2,4,6）.
