Computational issues in the solution of liquid crystalline polymer flow problems.

摘要

This dissertation considers the computational issues that arise in the simulation of the flow of certain complex fluids, such as Liquid Crystalline Polymers. The computational effort required in these calculations can be tremendous, and this makes the development of efficient algorithms imperative. We first describe the use of Smoothed Particle Hydrodynamics techniques for this problem. The most time consuming aspect of this computation is in the nonparametric density estimation that is involved in these calculations. We propose a fast estimator for this purpose. We also show that the computational structure of the SPH technique is related to that of particle methods with short-range interactions, and develop a domain decomposition scheme for particle methods on the sphere, which can be used in parallel algorithms. We finally discuss the implementation issues in our scheme for finite difference computations of two dimensional flows. Specifically, we address the issues of the management of adaptive meshes, parallelization and load balancing.