A DLM/FD/IB Method for Simulating Compound Cell Interacting with Red Blood Cells in a Microchannel

In this article, a computational model and related methodologies have been tested for simulating the motion of a malaria infected red blood cell (iRBC for short) in Poiseuille flow at low Reynolds numbers. Besides the deformability of the red blood cell membrane, the migration of a neutrally buoyant particle (used to model the malaria parasite inside the membrane) is another factor to determine the iRBC motion. Typically an iRBC oscillates in a Poiseuille flow due to the competition between these two factors. The interaction of an iRBC and several RBCs in a narrow channel shows that, at lower flow speed, the iRBC can be easily pushed toward the wall and stay there to block the channel. But, at higher flow speed, RBCs and iRBC stay in the central region of the channel since their migrations are dominated by the motion of the RBC membrane.     

Numerical Simulation of Red Blood Cell Suspensions Behind a Moving Interface in a Capillary

Computational modeling and simulation are presented on the motion of red blood cells behind a moving interface in a capillary. The methodology is based on an immersed boundary method and the skeleton structure of the red blood cell (RBC) membrane is modeled as a spring network. As by the nature of the problem, the computational domain is moving with either a designated RBC or an interface in an infinitely long two-dimensional channel with an undisturbed flow field in front of the computational domain. The tanking-treading and the inclination angle of a cell in a simple shear flow are briefly discussed for the validation purpose. We then present and discuss the results of the motion of red blood cells behind a moving interface in a capillary, which show that the RBCs with higher velocity than the interface speed form a concentrated slug behind the moving interface.     

Numerical study on bacterial flagellar bundling and tumbling in a viscous fluid using an immersed boundary method

The bundling and tumbling behavior of bacterial flagella in a viscous fluid has got immense significance in the field of biological fluid dynamics. In this paper we investigate the hydrodynamic interaction among two and more than two flagella in a viscous fluid based on an immersed boundary method. We model each helical flagellum by a number of triangular cross-sections with three immersed boundary (IB) points on each cross-section. Three types of elastic links are generated from each IB point to create an elastic network model of the flagellum and the first cross-section is modeled as the flagellar motor. The elastic forces are computed based on the elastic energy approach and the motor forces are obtained from the applied angular frequency of rotation of the motor. The Stokes equations governing the flow are solved on a staggered Cartesian grid system using a fractional-step based finite-volume method. It is observed that when two left-handed helical flagella rotate in the counter-clockwise direction, the resulting hydrodynamic interaction leads to bundling. When one of the flagella reverses the direction of rotation to clockwise the hydrodynamic interaction results in tumbling. During the bundling, the flagella wrap and intertwine each other, whereas during the tumbling they separate in an erratic way. There exists an exact combination of the handedness and rotational direction of the flagella to achieve the bundling. The bundling-to-tumbling behavior of the flagella is studied and it is concluded that the tumbling occurs faster than the bundling. Further, the hydrodynamic interaction among three flagella in a viscous fluid is studied for the cases of rotation in the same direction and in different directions. The bundling and tumbling behavior is well captured even for the case of multiple (more than two) flagella using the developed model.     

分析表面裂纹的一种新方法

本文作者综合了线弹簧模型及边界元法的优点,开发了一种新的线弹簧边界元法.该方法把表面裂纹这一三维问题简化为拟一维问题,可用于分析受到多种载荷作用的含表面裂纹的板.本文对该方法进行了理论分析和数值验证,报告了计算结果.结果表明,该方法经济有效.利用该方法仅使用个人计算机就可以分析表面裂纹问题.     

数学物理中的总体和局部场GL方法

为了求解物理化学生物材料和金融中的微分方程,提出了一种总体(Global)和局部(Local)场方法.微分方程的求解区域可以是有限域,无限域,或具曲面边界的部分无限域.其无限域包括有限有界不均匀介质区域.其不均匀介质区域被分划为若干子区域之和.在这含非均匀介质的无限区域,将微分方程的解显式地表示为在若干非均匀介质子区域上和局部子曲面的积分的递归和.把正反算的非线性关系递归地显式化.在无限均匀区域,微分方程的解析解被称为初始总体场.微分方程解的总体场相继地被各个非均匀介质子区域的局部散射场所修正.这种修正过程是一个子域接着另个子域逐步相继地进行的.一旦所有非均匀介质子区域被散射扫描和有限步更新过程全部完成后,微分方程的解就获得了.称其为总体和局部场的方法,简称为GL方法.GL方法完全地不同于有限元及有限差方法,GL方法直接地逐子域地组装逆矩阵而获得解.GL方法无需求解大型矩阵方程,它克服了有限元大型矩阵解的困难.用有限元及有限差方法求解无限域上的微分方程时,人为边界及其上的吸收边界条件是必需的和困难的,人为边界上的吸收边界条件的不精确的反射会降低解的精确度和毁坏反算过程.GL方法又克服了有限元和有限差方法的人为边界的困难.GL方法既不需要任何人为边界又不需要任何吸收边界条件就可以子域接子域逐步精确地求解无限域上的微分方程.有限元和有限差方法都仅仅是数值的方法,GL方法将解析解和数值方法相容地结合起来.提出和证明了三角的格林函数积分方程公式.证明了当子域的直经趋于零时,波动方程的GL方法的数值解收敛于精确解.GL方法解波动方程的误差估计也获得了.求解椭圆型,抛物线型,双曲线型方程的GL模拟计算结果显示出我们的GL方法具有准确,快速,稳定的许多优点.GL方法可以是有网,无网和半网算法.GL方法可广泛应用在三维电磁场,三维弹塑性力学场,地震波场,声波场,流场,量子场等方面.上述三维电磁场等应用领域的GL方法的软件已经由作者研制和发展了。     

A Generalized Nonclassical Model of Stress-Strain State in the Problems of Statics,Dynamics, and Contact Interaction of Layered Plates and Shells

A new generalized two-dimensional nonclassical model for the dynamic stress-strain state of layered anisotropic plates and shallow shells is constructed. A feature of the model is the complete account of the factors which represent the spatial character of their deformation; in particular, the transverse shear and transverse compression strains as well as the geometrical nonlinearity and dynamic action of the load are accounted for.