University of California, San Diego
Suspensions of deformable particles including bubbles, drops, and capsules are encountered in a wide variety of natural, engineering, and physiological systems. An example is provide by a common class of particulate physiological fluids with suspended biological cells, including blood. The numerical simulation of particle deformation under the influence of a specified internal or external flow presents a host of computational challeges associated with the accurate desription of the evolving interfacial shapes, and the successful coupling of the flow on either side of the interface. In this lecture, we review recent advances in three areas: Boundary-integral formulations for low-Reynolds number hydrodynamics; adaptive regridding of evolving interfaces by the advancing-front method; coupling of the viscoelastic tensions developing on generalized interfaces to the fluid tractions exerted on them; and advanced techniques for the dynamical simulation of suspensions with a large number of suspended particles.