Algorithms for Simulating Flows with Elastic Components

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

This project considers the construction and analysis of algorithms to simulate fluid systems containing elastic components. Polymers, such as liquid crystals, are an important class of such fluids, and in this instance the elastic properties of the molecules are usually incorporated into a continuum model. Another example is blood flow where the elasticity of the red blood cells gives rise to non-Newtonian behavior. This problem was motivated by collaborative work with engineers who wish to determine the distribution of and damage to red blood cells in the small clearances within mechanical heart assist devices. Since these clearances are of comparable dimension to the cells, it is necessary to explicitly model the cells at the micrometer scale in order to determine their distribution and the stresses they experience. The mathematical structure of the equations 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 is a key technology required for the design and development of many "next generation" products, such as micro-mechanical devices, bio-materials, and prosthetic organs. For example, a major mode of failure in mechanical heart assist devices is the formation of clots (thrombosis) which are primarily initiated by damage to the red blood cells. This phenomena is difficult to control and the ability to simulate it on a computer it would represent a breakthrough which would eliminate much of the expensive and time consuming experimentation currently required. The equations used to model such phenomena are complex and poorly understood, and much of the research proposed herein is directed to revealing the theoretical (mathematical) properties of these models. This work complements the more practical approaches undertaken in the engineering community and at the national laboratories.