J. of Non-Newtonian Fluid Mechanics, 70 (1997), pp. 125--154.
C. Chaubal, Ö. Egecioglu, G. Leal, and A. Srinivasan
Smoothed Particle Hydrodynamics techniques for the solution of kinetic theory problems. Part 1: Method
Abstract.
The Smoothed Particle Hydrodynamics (SPH) technique has been applied to
a problem in kinetic theory, namely, the dynamics of liquid
crystalline polymers (LCP). It is a Lagrangian solution method
developed for fluid flow calculations; its adaptation to kinetic
theory is straightforward. The Lagrangian formulation
of the Doi theory for LCPs is first described. The problem is
presented in the general framework of nonparametric density
estimation. The implementation of the
SPH technique in this particular problem is given. We discuss
particular aspects of our implementation of SPH, including the form
of the kernel function and use of the adaptive kernel. We then
present results which demonstrate convergence and other details of the
solution method, and also make comparisons with other solution
techniques for this problem.
omer@cs.ucsb.edu