斯托克斯流中避免接触粒子的障碍方法
A Barrier Method for Contact Avoiding Particles in Stokes Flow
AI总结：
本文提出一种基于障碍能量的方法，通过施加最小排斥接触力来避免斯托克斯流中刚性粒子的重叠，并在球、杆和回旋镖形粒子悬浮液中验证了无碰撞模拟的有效性。
摘要：
斯托克斯流体中的刚性粒子在物理上不可能重叠，因为一层薄流体总是将粒子对分开，随着间距减小，流体会对物体施加越来越强的排斥力。在数值上，即使对于中等系统规模，解析这些润滑力的代价也高得难以承受。因此，无论选择何种求解斯托克斯方程的方法，通常都无法保证在动力学模拟中不发生粒子碰撞和重叠。在这项工作中，非重叠约束以粒子上边界点之间的欧几里得距离的形式，通过障碍能量来表示。我们求解任意接触粒子对之间排斥接触力的最小幅值，以通过在下一个时间层强制障碍能量为零来修正重叠，前提是前一个时刻的构型是无接触的。该方法使用多球（multiblob）方法求解斯托克斯流中的迁移率问题，并应用于球体、杆状和回旋镖形粒子悬浮液进行测试。在所有时刻都获得了无碰撞构型。文中还展示了在自然促进粒子相互作用的背景流中，接触力对一组杆状粒子集体有序性的影响。
英文摘要：
Rigid particles in a Stokesian fluid can physically not overlap, as a thin layer of fluid always separates a particle pair, exerting increasingly strong repulsive forces on the bodies for decreasing separations. Numerically, resolving these lubrication forces comes at an intractably large cost even for moderate system sizes. Hence, it can typically not be guaranteed that particle collisions and overlaps do not occur in a dynamic simulation, independently of the choice of method to solve the Stokes equations. In this work, non-overlap constraints, in terms of the Euclidean distance between boundary points on the particles, are represented via a barrier energy. We solve for the minimum magnitudes of repelling contact forces between any particle pair in contact to correct for overlaps by enforcing a zero barrier energy at the next time level, given a contact-free configuration at a previous instance in time. The method is tested using a multiblob method to solve the mobility problem in Stokes flow applied to suspensions of spheres, rods and boomerang shaped particles. Collision free configurations are obtained at all instances in time. The effect of the contact forces on the collective order of a set of rods in a background flow that naturally promote particle interactions is also illustrated.
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