Slender and Close - Accurate Stokes Flows for Rigid Particles in Challenging Geometries

Explore advanced numerical methods for modeling rigid particle suspensions in viscous fluids through this distinguished mathematics lecture. Learn about two groundbreaking computational tools that address critical challenges in Stokes flow simulations, particularly when particles become extremely close together or have slender geometries. Discover how interior fundamental solutions augmented with image systems can accurately handle sphere separations down to thousandths of their radius, and examine a novel boundary integral scheme for slender fibers that achieves convergent solutions with up to 10 accurate digits. Understand the limitations of traditional slender body theory and see how these new methods overcome non-convergence issues while maintaining high-order accuracy. Examine applications to sedimentation, rheology, microfluidic devices, active matter, and bacterial transport, with demonstrations of well-conditioned iterative solutions and near-linear cost scaling. Gain insights into block-diagonal least-squares preconditioning for large collections of spheres and ellipsoids, adaptive quadrature techniques, and high-order time-stepping methods for dynamic simulations.