A NUMERICAL-METHOD FOR SUSPENSION FLOW

Peskin's (J. Comput. Phys. 25, 220, 1977) immersed boundary technique is modified to give a new numerical method for studying a fluid with suspended elastic particles. As before, the presence of the suspended particles is transmitted to the fluid through a force density term in the fluid equations. As a result, one set of equations holds in the entire computational domain, eliminating the need to apply boundary conditions on the surface of suspended objects. The new method computes the force density by discretizing the stress-strain constitutive equations for an elastic solid on a grid, using data provided by clusters of Lagrangian points. This approach clearly specifies the material properties of the suspended objects. A simple data structure for the Lagrangian points makes it easy to model suspended solids with arbitrary shape and size. The method is validated by comparing numerical results for elastic vibrations and particle settling in viscous fluids, with theory and analysis. The capability of the method to do a wide range of problems is illustrated by qualitative results for lubrication and cavity flow problems. © 1991.