A Fully-Implicit Spectral Boundary Element Algorithm for Capsules and Biological Cells

国家科学基金会-化学运输系统分部-颗粒多相过程计划（1415）提案编号：0730811主要研究者：Dimitrakopoulos，Panagiotis附属机构： 马里兰州大学提案标题：胶囊和生物细胞的全隐式谱边界元算法本提案的目标是开发一种新的三维计算算法，这将有助于研究Stokes流中膜封闭流体体积（如人工胶囊，囊泡和生物细胞）的动力学。这些系统在广泛的工业和生理过程中遇到，因此它们的研究是一个具有重大技术和根本意义的问题。然而，由于界面膜的流体力学性质与固体力学性质的耦合，这些系统的动力学行为是一个相当复杂的计算问题。这清楚地反映在一个事实，即存在相当有限的计算结果的三维问题，涉及胶囊，囊泡和红细胞（RBC）。现有技术算法的使用受到限制，因为（a）它们采用低阶插值方案，导致低精度和/或高计算成本（由于密集网格）;（B）它们还采用显式时间积分方案来确定界面位置，导致小时间步长（由于稳定性考虑）;和/或（c）在多处理器计算机上可能显示有限的可扩展性。为了克服这些障碍，我们建议扩展我们的高效，雅可比自由，三维全隐式，光谱边界元算法的液滴动力学的膜状接口的情况下。本质上，我们将用更复杂的膜的界面条件来代替液滴的简单界面条件（由于表面张力）。在我们的算法中，这些边界条件的纳入是一个简单但繁琐的过程，因为膜张力涉及复杂的非线性函数的高阶界面几何导数。我们强调，我们的全隐式算法可以处理任何非线性边界/界面条件和约束;这些方程通过在某个时刻涉及未知形状的边界扰动，与形状演变耦合，然后通过迭代，我们求解满足这些条件的界面形状。该算法能够准确有效地确定所有膜的界面性质（包括剪切、面积扩张和弯曲张力），利用大的时间步长，从而为涉及三维胶囊、囊泡和生物细胞的最复杂问题产生高质量的结果。因此，我们的新方法克服了由最先进的算法的状态所施加的限制，而它有利于调查的一个更现实的和复杂的问题，目前被认为是unreachable.Broader的影响这一建议的算法有潜力显着增加我们的物理知识的胶囊，囊泡和红细胞的动力学，这将在制药行业产生广泛的影响，生理学和生物力学。研究生将参加P.I.的研究转移所获得的知识。该提案的结果将被纳入马里兰州大学的教育计划，并将通过科学会议、期刊出版物和网络广为人知。

National Science Foundation - Division of Chemical &Transport Systems - Particulate & Multiphase Processes Program (1415)Proposal Number: 0730811 Principal Investigators: Dimitrakopoulos, Panagiotis Affiliation: University of Maryland Proposal Title: A Fully-Implicit Spectral Boundary Element Algorithm for Capsules and Biological Cells The goal of this proposal is to develop a novel three-dimensional computational algorithm that will facilitate the study of the dynamics of membrane-enclosed fluid volumes (such as artificial capsules, vesicles and biological cells) in Stokes flow. These systems are encountered in a broad range of industrial and physiological processes, and thus their study is a problem of great technological and fundamental interest. However, the dynamic behavior of these systems is a rather complicated computational problem due to the coupling of the fluid mechanics with the solid mechanics properties of the interfacial membrane. This is clearly reflected in the fact that there exist rather limited computational results for three-dimensional problems involving capsules, vesicles and red blood cells (RBCs). The use of the state of the art algorithms is restricted because (a) they employ low-order interpolation schemes resulting in low accuracy and/or high computational cost due to dense grids; (b) they also employ explicit time integration schemes for determining the interfacial position resulting in small time steps due to stability considerations; and/or (c) may show limited scalability on multiprocessor computers. To overcome these obstacles, we propose to extend our efficient, Jacobian-free, three-dimensional fully implicit, spectral boundary element algorithm for drop dynamics to the case of membrane-like interfaces. In essence we will replace the simple interfacial condition for a droplet (due to surface tension) with the more complicated membrane's interfacial conditions. The incorporation of these boundary conditions in our algorithm is a straightforward but tedious process since membrane tensions involve complicated non-linear functions of high-order interfacial geometric derivatives. We emphasize that our fully-implicit algorithm can handle any non-linear boundary/interfacial condition and constraint; these equations are linearized via boundary perturbations involving the unknown shape at some time instance, coupled with the shape evolution, and then via iterations we solve for the interfacial shape which satisfy these conditions/constraints to any desired precision.Intellectual Merit The proposed algorithm has the ability to determine accurately and efficiently all the membrane's interfacial properties (including shearing, area dilation and bending tensions), utilize large time steps, and thus produce high-quality results for the most complicated problems involving three-dimensional capsules, vesicles and biological cells. Therefore, our novel methodology overcomes the limitations imposed by the state of the art algorithms, while it facilitates the investigation of a vast array of more realistic and complicated problems which currently are regarded as unattainable.Broader Impact This proposed algorithm has to potential to significantly increase our physical knowledge on the dynamics of capsules, vesicles and RBCs which will have a broad impact in the pharmaceutical industry, physiology and biomechanics. Graduate students will participate in the P.I.'s research transferring the acquired knowledge. The results of this proposal will be integrated into the education program of the University of Maryland, and they will become generally known via scientific meetings, journal publications and the web.