Algorithms for Simulating Flows with Elastic Components

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This project considers the construction and analysis of algorithms tosimulate fluid systems containing elastic components. Polymers, suchas liquid crystals, are an important class of such fluids, and in thisinstance the elastic properties of the molecules are usuallyincorporated into a continuum model. Another example is blood flowwhere the elasticity of the red blood cells gives rise tonon-Newtonian behavior. This problem was motivated by collaborativework with engineers who wish to determine the distribution of anddamage to red blood cells in the small clearances within mechanicalheart assist devices. Since these clearances are of comparabledimension to the cells, it is necessary to explicitly model the cellsat the micrometer scale in order to determine their distribution andthe stresses they experience. The mathematical structure of theequations modeling viscoelastic polymers and blood are very similar,and insight gained in one of them sheds light on the other.The ability to simulate the flow of complex materials on a computer isa key technology required for the design and development of many "nextgeneration" products, such as micro-mechanical devices, bio-materials,and prosthetic organs. For example, a major mode of failure inmechanical heart assist devices is the formation of clots (thrombosis)which are primarily initiated by damage to the red blood cells. Thisphenomena is difficult to control and the ability to simulate it on acomputer it would represent a breakthrough which would eliminate muchof the expensive and time consuming experimentation currentlyrequired. The equations used to model such phenomena are complex andpoorly understood, and much of the research proposed herein is directedto revealing the theoretical (mathematical) properties of thesemodels. This work complements the more practical approaches undertakenin the engineering community and at the national laboratories.