一种模拟三维红细胞变形的前向跟踪式格子Boltzmann方法  

A Front-tracking Lattice Boltzmann Method for Simulating 3D Capsule Erythrocyte Deformation

作　　者：杨婷[1] 魏守水[1] 崔建强[1] 

机构地区：[1]山东大学控制科学与工程学院,济南250061

出　　处：《中国生物医学工程学报》2011年第3期388-397,共10页Chinese Journal of Biomedical Engineering

基　　金：国家自然科学基金(51075243)

摘　　要：将前向跟踪法与晶格波尔兹曼法相结合,研究三维双凹碟形胶囊式红细胞的变形。将红细胞模拟为内含牛顿流体的双凹碟形弹性薄膜胶囊,将薄膜内外的液体看做是具有不同物理特性的流体;使用晶格波尔兹曼方法的多块策略,改善细胞模型附近的网格,增加三维计算的准确度和效率。使用的细网格仅覆盖每个计算轴的40%,较同时选用离散为连接4 098个点的8 192个三角元的细胞薄膜模型,这不仅可以提高网格分辨率,而且还能节省计算时间。从理论上证明,在雷诺数不大于0.25的剪切流中,惯性作用对细胞变性的影响很小,同时得到无因次参数为0.05、细胞内外黏度比为0.2时三维健康红细胞的360°稳定坦克履行为。不仅成功模拟了惯性作用下典型的三维红细胞坦克履行为,而且使用的细网格仅占整个计算区域的6.4%,在保证计算准确度的同时,提高了计算效率,为模拟三维红细胞变形提供了一种更加可行的途径。This article combined lattice Boltzmann method with the front-tracking method to study the 3D deformation behaviour of biconcave discoid capsule RBC model.The RBC model was choser as an elastic biconcave discoid thin membrane capsule containing Newton fluid.Fluids have different physical properties in and outside of the RBC model thus eliminating one previous limit that all fluid must have the same properties.Multi-block strategy of LBM was used to improve the grid around the RBC model for the sake of increasing the 3D computational accuracy and efficiency.In this method,thin grid covered only 40% of each calculation shaft,and a cell membrane model discreting 8 192 triangle elements connecting 4 098 points was chosen,which not only improved the grid resolution,but also saved calculation time.It was theoretically proved that the inertia effect on red blood cells deformation in shear flow was small when Reynolds number was less than 0.25.The 360°stable tank-treading motion of normal red blood cells was simulated under the condition that non-dimensional parameter was 0.05 and the ratio of the viscosity inside and outside erythrocyte was 0.2.In addition to simulating typical three-dimensional erythrocyte tank-treading motion under inertial function,our study improves the calculation accuracy and efficiency using fine meshes covered only 6.4% of the whole calculation area,providing a more feasible approach for simulating the three-dimensional erythrocyte deformation.

关 键 词：多块晶格波尔兹曼方法 前向跟踪法 双凹碟形红细胞模型 惯性作用 坦克履行为 

分 类 号：R318.08[医药卫生—生物医学工程]