多尺度随机Eulerian-Lagrangian方法

The immersed boundary method has been widely used in modeling fluid-structure interaction systems. At the length scale of nano-particles, thermal energy of the aqueous environment becomes significant, and the whole system is subjected to thermal fluctuation. The Stochastic Eulerian Lagrangian Method (SELM), an extension of immersed boundary method to include thermal fluctuations, was developed to solve these problems. However, only temporal and spatial uniform finite difference method has been developed, which greatly limits the application of the method. By introducing both temporal and spatial multiscale technique, we can not only use fine mesh to accurately tracking the detailed movement of the flexible structure while use the coarse mesh to resolve the parts far away from the interested regime, but also introduce new molecular dynamics model to account for the interactions between structure-structure interaction, so that a more accurate method for modeling nano-structures immersed in a fluid can be applied at a relatively lower computational cost. Success of this proposal will not only have a direct impact on development of numerical methods for fluid-structure interaction problems, but also can be widely used in biology, medicine, and material science etc. One direct application is target drug delivery.

侵入边界方法被广泛的应用于流固耦合问题的数值模拟，但当所研究的固体到微观尺度或更小的时候，热能的影响将变得不可忽略，固体和液体将同时收到热扰动的影响。据此，基于侵入边界方法的随机Eulerian-Lagrangian方法（SELM）被开发出来解决这类问题。通过引入多尺度时间空间方法，既可以通过使用细网格更精确追踪固体边界的运动而对远离固体表面的液体部分实行粗网格计算，又可以通过对感兴趣的细分网格区域引入小尺度的时间步骤来模拟出固体结构局部变化，同时，还可以在小范围能引入分子动力学模型来描述固体颗粒之间的相互作用力，从而以较小的计算成本来更准确的模拟微观尺度下固体在液体中的运动。本项目预期成果不仅在数值计算方法开发上具有重要意义，而且可以广泛的应用到生物学，医学和材料学等领域，其中一个主要应用便是靶式药物在血管中的传递问题。

本项目主要开发和应用基于侵入边界方法的随机欧拉拉格朗日方法。主要结果包括，开发了随机欧拉拉格朗日方法的算法在不同边界条件下的应用，并引入自适应网格以提升对特定问题的计算速度，同时探寻了图形计算显卡对提升计算速度的影响，其中一部分已经开源。在应用上，我们探究了微椭球体在管道中的动力学特征，研究了不同横纵轴比的椭球及椭球与管道壁距离之间的影响；固体颗粒间浓度对与其扩散系数的影响，考察了硬球和软球模型下，随固体颗粒浓度的增加对扩散系数的不同影响；此外，我们还尝试和物理实验相结合，探究固体颗粒对打印喷射流的一些影响。