液滴在固体平表面上均匀蒸发过程的格子Boltzmann模拟

通过格子玻尔兹曼(lattice Boltzmann method,LBM)数值模拟,研究了液滴在固体平表面上蒸发过程形状变化的机理.揭示了不同静态接触角下液滴蒸发过程中重力对其形状变化的影响规律.结果表明,重力的影响随着液滴尺度的减小而减弱,达到某一临界点后,重力对蒸发过程的影响可以忽略.模拟定量确定了液滴尺寸的这一临界值,并分析了蒸发过程中几个典型时刻液滴内部的流场分布,进一步研究了重力的影响.     

层射流的格子Boltzmann方法的数值模拟

通过引入一种格子Boltzmann方法的特殊边界处理,对对称和非对称的层射流进行有效的数值研究,模拟结果与已有的数值结果非常吻合.表明了格子Boltnnann方法解层射流问题的高效与稳定.     

格子Boltzmann方法解扩散方程的复杂边界条件研究

对格子Boltzmann方法求解含第三类边界条件的扩散方程进行了理论和数值研究,构造了一种新的基于bounce-back的边界处理数值格式,用来处理复杂边界问题.借助渐近分析,证明了新方法的数值相容性.用数值算例从不同角度分析了算法的精度和稳定性等,与已有算法相比,新方法在精度、稳定性和效率方面均有较大提高.最后通过一个复杂边界反应扩散的示例演示了新方法应用于复杂多孔介质内多物理化学输运模拟的可行性和有效性.     

前后排列旋转圆柱体对流热交换的格子Boltzmann方法解

用格子Boltzmann方法,数值研究流过前后排列两旋转圆柱体的二维层流．用二阶精度的速度场和温度场,数值化涉及运动的曲线边界．在Reynolds数为100,Prandtl数为0.71时,研究旋转速度比的变化和不同间距的影响．在4种不同间距(3, 1.5, 0.7, 0.2)下,研究旋转速度比的不同范围．结果表明,当间距取大数值时,第1个圆柱体的升力和阻力系数,与单个圆柱体相类似;对所有间距(除间距3以外),第2个圆柱体的升力系数,随着角速度的增加而减小,而阻力系数反而增加．圆柱体表面平均周期Nusselt数的结果表明,当两圆柱体间距小且角速度又低时,热传导是主要的传热机理,而当间距大且角速度又高时,对流是主要的传热机理．     

大功率LED荧光粉硅胶点涂工艺的三维格子Boltzmann模拟

为实现蓝光LED(light emitting diode)芯片向白光LED照明的转化,大功率LED封装工艺流程中存在一个关键的环节——荧光粉涂覆,即通过点涂方式将荧光粉硅胶涂覆于LED芯片周围.荧光粉硅胶涂覆工艺是一个两相流动过程,它直接决定了荧光粉硅胶层的几何形貌及物理特性,并影响LED最终的光学和热学性能;因此对其中流动过程物理机制的理解有利于提升荧光粉涂覆质量,实现高性能LED产品.基于格子Boltzmann方法,建立荧光粉硅胶流动模型,并应用该模型研究了在平坦表面和方形凸起结构两种封装形式上的荧光粉硅胶点涂成形流动过程.结果表明:格子Boltzmann方法能够准确地模拟荧光粉点涂流动过程;在平坦表面上荧光粉硅胶液滴接触线与液滴直径之比(dL/D)和相对时间(t/T)成幂函数关系.     

空间分数阶电报方程的格子Boltzmann方法

应用格子Boltzmann方法（LBM）对Riemann Liouville空间分数阶电报方程进行了数值模拟研究.首先,将分数阶算子中的积分项进行离散化处理,并进行了收敛阶分析.然后,构建了带修正函数项的一维三速度(D1Q3)的LBM演化模型.利用Chapman Enskog多尺度技术和Taylor展开技术,推导出各平衡态分布函数和修正函数的具体表达式,准确地从所建的演化模型恢复出宏观方程.最后,数值计算结果表明该模型是稳定、有效的.     

两球形颗粒间横向毛细力的格子Boltzmann研究

采用以Shan-Chen多组分模型为基础的格子Boltzmann-伪固体模型对两颗粒间的浮体和浸润横向毛细力展开数值模拟研究,其中流体-固体间的相互作用及颗粒润湿性质在介观层次上采用简单形式得以充分考虑．三维测试表明,与已有理论解相比,成功再现了横向毛细力与颗粒间距的“1/L”关系,并确认了浸润横向毛细力与表面张力间的线性关系．这表明可进一步应用该模型研究横向毛细力作用下的颗粒自聚集等现象.     

多孔介质中两相驱离的格子Boltzmann模型新研究

利用粒子之间相互作用,即同种物质粒子相互吸引,异种物质粒子相互排斥这一物理化的原理研究并提出了一个新型的模拟多孔介质中二相驱离的格子玻耳兹曼模型,结果表明它能有效地模拟多孔介质中的二相驱离问题,且节省机时,分界面上涨落也小,不必采取任何平均措施.     

T型微通道内液滴在幂律流体中运动机理的格子Boltzmann方法研究北大核心CSCD

采用非Newton不可压两相流格子Boltzmann模型研究了T型微通道内Newton液滴在非Newton幂律流体中的运动过程.研究了非Newton流体幂律指数n、主管道毛细数Ca、两相流量比Q、两相黏度比M以及主管道壁面润湿性θ对液滴在T型微通道内的形成尺寸、形成时间和变形参数(DI)的影响.研究结果表明:首先,主管道流体幂律指数n从0.4增加到1.6时,液滴的形成尺寸近似呈线性减小,而液滴的形成时间和变形参数先快速减小,然后缓慢减小;其次,黏度比对液滴形成尺寸、液滴形成以及变形参数的影响与幂律指数的影响基本一致;再者,随着Ca和主管道壁面润湿性的增加,形成液滴的尺寸近似呈线性减小,形成液滴的时间和变形参数先快速减小然后缓慢减小,且减小趋势随幂律指数的增加而减缓;最后,研究结果还表明主管道和子管道的流量比Q越大,液滴形成时间越长,液滴形成尺寸和变形参数越小.     

基于多GPU的格子Boltzmann法对槽道湍流的直接数值模拟

采用多GPU并行的格子Boltzmann方法（lattice Boltzmann method, LBM）对充分发展的槽道湍流进行了直接数值模拟．GPU(graphic processing unit)的数据并行单指令多线程（single-instruction multiple-thread, SIMT)特征与LBM完美的并行性相匹配,使得LBM求解器在GPU上运行获得了极高的性能,亦使得大规模DNS(direct numerical simulation)在桌面级计算机上进行成为可能．采用8个GPU,网格数目达到6.7×107,全场网格尺寸Δ+=1.41．模拟3×106个时间步长,用时仅24 h．另外,直接模拟结果无论是在平均流速或湍流统计量上均与Moser等的结果吻合得很好,这也证实了二阶精度的格子Boltzmann法直接模拟湍流的能力与有效性     

Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis北大核心CSCD

接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同,是两相流体在润湿表面上流动的重要现象.该文采用改进的伪势格子Boltzmann(LB)多组分模型,并与几何润湿边界条件相结合,研究了两个液滴在具有接触角滞后性微通道表面上的运动行为,主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响.研究结果表明：毛细数的增大有助于液滴的移动,然而并不利于液滴的排出,且毛细数的增加对上游液滴的影响大于其对下游液滴的影响;另一方面,接触角滞后性窗口越大,液滴运动和形变更迟缓,但形变程度更明显,两液滴更早地发生合并,但更晚地排出管道;液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式,但都导致通道中残留小液滴,使得液滴排出通道的时间增加.研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大,越不利于液滴排出管道.     

Lattice Boltzmann simulation for the spiral waves in the excitable medium

We propose lattice Boltzmann method for the spiral waves. Using Chapman-Enskog expansion and multiscales technique, we obtain equilibrium distribution functions of the model. As an example, we simulate the Selkov reactions with scratching mark, i. e. using a scratching mark pacemaker, obtained one classical spiral waves.     

Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force Using a Lattice Boltzmann Fictitious Domain Method

Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs, which motivates us to model the sedimentation of red blood cell (RBC) under strong external magnetic body force. To model the sedimentation of a RBC in a square duct and a circular pipe, a recently developed technique derived from the lattice Boltzmann and the distributed Lagrange multiplier/fictitious domain methods (LBM-DLM/FD) is extended to employ the mesoscopic network model for simulations of the sedimentation of a RBC in flow. The flow is simulated by the LBM with a strong magnetic body force, while the network model is used for modeling RBC deformation. The fluid-RBC interactions are enforced by the Lagrange multiplier. The sedimentation of RBC in a square duct and a circular pipe is simulated, which demonstrates the developed method's capability to model the sedimentation of RBCs in various flows. Numerical results illustrate that the terminal settling velocity increases incrementally with the exerted body force. The deformation of RBC has a significant effect on the terminal settling velocity due to the change in the frontal area. The larger the exerted force, the smaller the frontal area and the larger the RBC deformation become. Additionally, the wall effect on the motion and deformation of RBC is also investigated.     

Mesoscopic Numerical Study on Flow Boiling Heat Transfer Performance in Channels With Multiple Rectangular Heaters北大核心CSCD

The flow boiling phenomenon in a channel with multiple rectangular heaters under a constant wall temperature was numerically studied with the lattice Boltzmann method. The effects of spacings between heaters, heater lengths and heater surface wettabilities on the bubble morphology, the bubble area and the heat flux on the heater surface, were studied. The results show that, the bubble growth rate increases with the spacing between heaters. The larger the bubble area is, the earlier the nucleated bubbles will leave the heater surface. The corresponding boiling heat transfer performance increases by 12% with the spacing between heaters growing from 250 lattices to 1 000 lattices. On the other hand, the longer the heater length is, the earlier the bubble will nucleate and leave the heater surface, and the better the boiling heat transfer performance will be. The boiling heat transfer performance increases by 13% with the heater length rising from 16 lattices to 22 lattices. In addition, the bubble nucleates later on the hydrophilic surface than on the hydrophobic surface. Compared with the hydrophilic surface, the hydrophobic surface retains residual bubbles after the leaving of bubbles from the heater. The average heat flux and the bubble area of the hydrophilic surface are less than those of the hydrophobic surface. With the contact angle changing from 77° to 120°, the heat transfer performance increases by 26%. Finally, the orthogonal test results indicate that, the wettability of the heat exchanger surface has the greatest influence on the flow boiling heat transfer performance, while the heater length has the least influence. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

偏微分方程求解的一种新颖方法-格子Boltzmann模型

介绍了一种偏微分方程求解的一种新颖方法格子Boltzmann模型,详细分析了它的基本理论和基本原理.并通过不可压Navier-Stokes方程组和二维含源项扩散方程的数值模拟计算实例,说明格子Boltzmann方法的有效性,展示了广阔的应用前景,为今后更深入的研究和广泛应用提供参考.     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

一种基于梯形模糊数的模糊多属性格序决策方法

从格序结构理论出发,根据梯形模糊数构成的集合按照一定的比较规则构成一偏序,进而满足一定条件构成格.给出了在应用具有梯形模糊数的多属性格序决策过程中格中缺失元素的补充机理.研究了用格序决策理论对梯形模糊数进行排序的方法,并将其用于投资者对投资方案的选择.