Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟

针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项u_xxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.     

Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟（英文）

针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项uxxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.     

一种新的模拟渗流运动的数值方法

根据格子Boltzmann方法及相关理论，建立了一个新的模拟渗流运动的数值模型，所得模型没有在边界上采取相应平均措施，同时还避免了一些非物理副产品的出现-实例计算数值结果与精确解符合较好，证明模型可靠- 关键词： 渗流 格子Boltzmann方法 数值模型     

三维方腔温盐双扩散的格子Boltzmann方法数值模拟

研究了温盐双扩散系统的多组分格子Boltzmann方法.通过对二维方腔的温盐双扩散系统的数值模拟，检验了方法的可行性及有效性，所得到的结果与差分法结果符合良好，继而将此方法推广到三维，建立了三维温盐双扩散系统的格子Boltzmann方法，对三维方腔双扩散问题进行了模拟和分析，并与差分法模拟的结果进行了比较，结果令人满意.最后，分析了格子Boltzmann方法在模拟双扩散对流问题时存在的局限性. 关键词： 格子Boltzmann方法 温盐双扩散 Boussinesq近似 数值模拟     

采用双分布函数格子Boltzmann方法的直流氩等离子体流动与传热分析

本文采用双分布函数格子Boltzmann方法(DDF-LB)模拟了直流氩电弧等离子体中的流动与传热问题。针对非局域热平衡状态下热等离子体中的原子、离子和电子三种组分,推导给出了不同组分的格子Boltzmann方程,通过耦合迭代求解得到各组分的温度和速度分布。文中采用随温度变化的松弛时间用以提高数值计算的稳定性。通过将本文的计算结果与文献结果进行比较,验证了DDF-LB方法求解等离子体中能量输运问题的稳定性和数值精度。     

基于格子Boltzmann方法的超声速非平衡流模拟

基于D1Q4可压缩格子Boltzmann模型,按照流通矢量分裂方法的思路,采用坐标旋转技术构造求解三维带化学反应Navier-Stokes方程对流通量求解器.结合有限体积法求解三维化学非平衡流Navier-Stokes方程,采用时间算子分裂算法解决化学反应刚性问题,数值模拟超声速化学非平衡流的三个经典算例.数值结果表明:在高马赫数下,采用D1Q4可压缩格子Boltzmann模型构造的三维对流通量求解器数值模拟中没有出现非物理解,同时在超声速化学非平衡流场中正确分辨激波、燃烧波等物理现象,精度和分辨率均较高,验证了本文构造的三维对流通量求解器的可靠性,拓宽了D1Q4可压缩格子Boltzmann模型的应用范围,为计算超声速化学非平衡流提供一种新方法.     

锌锅中低Pr流体混合对流的自维持振荡

本文对以带钢连续热镀锌为背景抽象出的锌锅中低Pr流体的流动和传热进行了数值模拟.数值结果显示,对Re=0的纯自然对流,Ra在104和105间时数值解由稳态解分岔为振荡解;对于Ra=0的纯强制对流,Re在4×103和5x1003之间时,数值解从稳态解分岔为振荡解;当Ra和Re均小于自然对流和强制对流单一机制作用时发生振荡的临界值时,混合对流的流动和传热为稳态;当Ra和Re中的一个参数大于单一机制作用发生振荡的临界值时,另一个参数由小于增加到大于单一机制作用发生振荡的临界值时,数值解由振荡解变为稳态解.     

用格子Boltzmann方法模拟MKDV方程

用精确到0(ε)的5速格子Boltzmann模型模拟MKDV方程:u_t+6u²u_x+u_xxx=0,并与MKDV方程的孤子解比较,二者精确吻合. 关键词： 格子Boltzmann方法 MKDV方程 孤子解     

基于LBM的多孔介质/流体交界面滑移效应细观研究

本文采用格子Boltzmann方法对真实多孔介质复合腔体内的自然对流进行了研究,分析了在不同瑞利数Ra、多孔介质厚度δ和高度Y条件下交界面处的滑移效应的变化规律。利用X-CT技术对真实多孔介质材料进行断层扫描,通过Matlab对图片进行处理并导入格子Boltzmann模型中进行求解。计算结果表明:当0.1Y0.9,复合腔体交界面速度滑移系数α和应力跳跃系数β随高度Y基本保持不变,而在靠近上下壁面时(Y0.1和Y0.9)变化明显;在一定的高度处,α和β均随Ra数发生缓慢变化;多孔介质的厚度δ对α和β影响较小。     

应用格子Boltzmann模型模拟一类二维偏微分方程

针对一类含源的二维非线性偏微分方程, 通过Chapman-Enskog展开技术和多尺度分析提出了带修正项的简单格子Boltzmann模型. 用模型模拟了几类二维偏微分方程, 数值模拟结果与精确解相符合. 成功将格子Boltzmann方法应用到二维偏微分方程的数值求解中. 关键词： 二维非线性偏微分方程 格子Boltzmann模型 Chapman-Enskog多尺度展开     

冰洲石晶体色散方程解析研究及折射率温度系数表达式

冰洲石晶体的主轴折射率随波长变化而变化。本文通过对Sellmeier方程严格求解．得出其系数表达式。经验证，折射率的计算值与实验值十分吻合。通过线性插值的方法求解出不同波长的温度系数表达式．从而得出不同温度不同波长的冰洲石晶体的主轴折射率，得到Sellmeier方程常数在各温度下的常数值。     

LBM simulation on natural convection flow in a triangular enclosure of green house under winter day conditions

Natural convection flow of roof top cross section in a green house has been numerically investigated using a thermal lattice Boltzmann method (TLBM). Two types of thermal boundary condition are considered; uniform and nonuniform bottom heating with symmetrically cold inclined walls. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for different Rayleigh number, Ra, ranging from 103 to 105 with other controlled parameters. The intensity of circulation is found to be higher and symmetric for lower values of Ra and the asymmetric behavior of the flow about the geometric centre line is seen for higher values of Ra in the case of uniform bottom heating. However, for nonuniform case, multiple circulation cells are observed for different Ra maintaining the symmetrical fluid properties. In addition, the average rate of heat transfer in terms of Nusselt number indicated the lower heat transfer rates for the nonuniform case compared to the uniform heating case. Finally, the results have been compared with the previous published works and found a good agreement.     

A curved no-slip boundary condition for the lattice Boltzmann method

We present a generalization of the no-slip boundary condition by Lätt et al. [J. Lätt, B. Chopard, O. Malaspinas, M. Deville, A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E 77 (5) (2008) 056703] from straight to curved geometries for the lattice Boltzmann Bhatnager–Gross–Krook method (LBGK). The boundary condition is based on a reconstruction of the populations from the density, velocity and rate of strain. For curved boundaries, the reconstruction reduces the question of accuracy to a technical issue of interpolation. We present a method of interpolation allowing a very accurate representation of the curved boundary. The resulting boundary condition is verified for three different test cases: Taylor–Couette flow in-between rotating cylinders, laminar flow around a cylinder and flow past an impulsively started cylinder, demonstrating its second order accuracy and low error constant. The present boundary is stable for relaxation frequencies close to two.     

Lattice Boltzmann simulation of 3-dimensional natural convection heat transfer of CuO/water nanofluids

The present study investigated fluid flow and natural convection heat transfer in an enclosure embedded with isothermal cylinder. The purpose was to simulate the three-dimensional natural convection by thermal lattice Boltzmann method based on the D3Q19 model. The effects of suspended nanoparticles on the fluid flow and heat transfer analysis have been investigated for different parameters such as particle volume fraction, particle diameters, and geometry aspect ratio. It is seen that flow behaviors and the average rate of heat transfer in terms of the Nusselt number (Nu) are effectively changed with different controlling parameters such as particle volume fraction (5 % ≤ φ ≤ 10 %), particle diameter (d _p = 10 nm to 30 nm) and aspect ratio (0.5 ≤ AR ≤ 2) with fixed Rayleigh number, Ra = 10⁵. The present results give a good approximation for choosing an effective parameter to design a thermal system.     

A solution-adaptive lattice Boltzmann method for two-dimensional incompressible viscous flows

A stencil adaptive lattice Boltzmann method (LBM) is developed in this paper. It incorporates the stencil adaptive algorithm developed by Ding and Shu [26] for the solution of Navier–Stokes (N–S) equations into the LBM calculation. Based on the uniform mesh, the stencil adaptive algorithm refines the mesh by two types of 5-points symmetric stencils, which are used in an alternating sequence for increased refinement levels. The two types of symmetric stencils can be easily combined to form a 9-points symmetric structure. Using the one-dimensional second-order interpolation recently developed by Wu and Shu [27] along the straight line and the D2Q9 model, the adaptive LBM calculation can be effectively carried out. Note that the interpolation coefficients are only related to the lattice velocity and stencil size. Hence, the simplicity of LBM is not broken down and the accuracy is maintained. Due to the use of adaptive technique, much less mesh points are required in the simulation as compared to the standard LBM. As a consequence, the computational efficiency is greatly enhanced. The numerical simulation of two dimensional lid-driven cavity flows is carried out. Accurate results and improved efficiency are reached. In addition, the steady and unsteady flows over a circular cylinder are simulated to demonstrate the capability of proposed method for handling problems with curved boundaries. The obtained results compare well with data in the literature.     

格点QCD中有限体积下形状因子的内插计算

在格点QCD的框架下,讨论了计算强子的形状因子的过程中,有限体积效应对所得结果的影响,并且给出了计算连续动量空间上形状因子数值的内插算法。本文以π介子的形状因子为例,介绍了从格点QCD中得到的三点关联函数出发计算π介子的形状因子的方法,并说明有限体积效应使得计算结果只能在分立动量上给出。本文探讨了一种保持旋转对称性的内插算法和一种对于傅立叶变换进行连续化的内插算法,基于分立的形状因子取值给出了连续动量空间上的形状因子,并且提供了模型模拟的结果与真实格点系统上的数值结果。本文提出的内插算法及数值模拟的结论不依赖于特定的格点系综,具有一定程度的普适性,能够推广到对于其他格点系统的有限体积效应的处理,同时为格点系统尺度的选取提供了有价值的参考。     

成像光谱仪辐射测量一致性校正中插值方法选择

谱线弯曲破坏了色散型成像光谱仪光谱辐射能量采集的一致性,采用插值的办法对系统采集到的辐射能最数据依据无偏离波长定标数据重新采样,可以提高光谱辐射测量的一致性.选择恰当的插值采样方法尤为重要,直接影响校止后辐射能量偏差的剩余量,决定了校正效果的好坏.采用常用的线性、三点二次多项式、四点三次Lagrange、五点四次Lag...     

格子-BOLTZMANN方法非均分网格的实施

本文提出了格子-Boltzmann方法的一种新的插值算法,使得网格划分与微观粒子运动方向相分离;用该方法模拟了后台阶通道内的突扩流动和二维极坐标下的空腔流.所得结果与传统方法吻合良好,证明了该方法的可行性.     

Bubble functions for the lattice Boltzmann method and their application to grid refinement

We present a new methodology of velocity field interpolation for the lattice Boltzmann method. The local information on spatial velocity gradients stored in the nodal momentum distribution function is exploited. We achieve quadratic interpolation order between neighboring nodes. Second-order bubble functions are derived from which the off-grid velocity field can be computed. A simple grid-refinement technique based on the bubble functions is introduced.     

The Bethe lattice spin glass revisited

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization. Received 27 September 2000