SMOOTHED PARTICLE HYDRODYNAMICS TECHNIQUES FOR THE SOLUTION OF KINETIC-THEORY PROBLEMS .1. METHOD

The smoothed particle hydrodynamics (SPH) technique has been applied t o a problem in kinetic theory, namely, the dynamics of liquid crystall ine polymers (LCPs). It is a Lagrangian solution method developed for fluid flow calculations; its adaption to kinetic theory is outlined. T he Lagrangian formulation of the Doi theory for LCPs is first describe d, and the problem is presented in the general framework of nonparamet ric density estimation. The implementation of the SPH technique in thi s specific problem is given, highlighting particular aspects of our im plementation of SPH, including the form of the kernel function and use of an adaptive kernel. We then present results which demonstrate conv ergence and other details of the solution method, and also make compar isons with other solution techniques and discuss other potential appli cations. (C) 1997 Elsevier Science B.V.