用格子Boltzmann模型模拟激波现象

根据微观和宏观之间的质量、动量、能量守恒准则,建立了一个两维的D2Q13格子Boltzmann模型,可从该D2Q13模型出发推导出宏观的流体力学方程,所得动量方程和Navier-Stokes方程相比,在黏性输运项上有明显的改进,用该模型对冲击波在障碍物表面上的折射和反射现象的数值模拟都得到了比较满意的结果,而且数值稳定性也很好.证明了D2Q13模型的适宜性 关键词： Boltzmann模型 分布函数 冲击波 流体力学方程     

Biot-Savart流体力学理论与索马里低空急流形成机理的研究

首先利用格子Boltzmann模型模拟了越赤道索马里低空急流对我国青藏高原东部大气环流的影响,再借助于Biot-Savart定律和流体力学理论以及美国国家环境预报中心的数据资料,研究分析了下垫面感热条件与索马里低空急流发生和发展的关系.太阳直射从南回归线逐渐向北移动过程中,索马里半岛和阿拉伯半岛地表温度逐渐增高;而在此期间,西北印度洋海表温度却增加缓慢.两半岛地表温度高的区域就会使空气上升,而海表低温区域空气就会下沉.海陆温差的增加有利于Rayleigh-Benard对流环流的生成和发展,也使得陆地和海面上正负垂直相对涡强度Γ增强.根据Biot-Savart定律,涡强度Γ的增强必然诱导出相应强大的水平速度.两半岛和海面上这一对正负相对涡度场耦合成一部高效率的"索马里抽气泵".这一抽气泵将气流从南半球吸入,在索马里沿岸附近排出.索马里半岛和阿拉伯半岛地表增温以及与西北印度洋海表温差是驱动索马里抽气泵运转的主要能源. 关键词： 索马里低空急流 Biot-Savart定律 索马里抽气泵     

格子Boltzmann模型的改进与流体力学方程

流体的流动可以看成是分子以上水平的粒子基本运动组合而成,任何一个粒子系统的Hamiltonian都是由动能和势能这两部分所组成.借助于Hamiltonian建立了微观粒子和宏观流体之间的能量守恒准则,发展了一个适合于热流场数值模拟的格子Boltzmann模型.从该模型可以还原出宏观的流体力学方程,所得动量方程的黏性输运项除了具有Navier-Stokes黏性力的特征外还与非定常的、非线性的动量通量和非定常的内能相关.用该模型对Benard热对流进行了数值模拟,很好地再现了Benard cell,并且克服了热格子Boltzmann模型数值稳定性差的不足.     

A Lattice Boltzmann Model for Two-Dimensional Magnetohydrodynamics

A lattice Boltzmann model （LBM） has been developed for simulating magnetohydrodynamics （MHD） along the line of Dellar [J. Comput. Phys. 179 （2002）95]. In this model the magnetic field is presented by a vector valued magnetic distribution function which obeys a vector Boltzmann equation. The truncated error of the equilibrium distribution in the present model is up to order O（u^4） in velocity u rather than the usual 0（u^3）. For verification, the model is applied to solve the shock tube problem and the main features of the flow predicted by the model are found to compare well with the corresponding results obtained with high-order semi-discrete schemes [J. Comput. Phys. 201 （2004） 261]. The numerical experiments have also shown that the present LBM model with the equilibrium distribution truncated at O（u^4） performs much better in terms of numerical stability than those truncated at O（u^3）.     

Heat Flux Boundary Conditions for a Lattice Boltzmann Equation Model

A method simplifying the external force term for the Boltzmann equation is proposed,using the Chapman-Enskog asymptotic expansion technique.The relationship between the perturbation strength parameter and the Grashof number is presented.A heat flux boundary condition for the temperature field simulation is developed according to the transforming ralations between the cold and hot particles on the boundary wall.The effects of buoyant force and the heat flux boundary condition are implemented with the two-particle systems of D2Q9 and D3Q15,and the numerical results agree well with the experimental result of silicone oil.