On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach

Abstract

Models of kinetic theory provide a coarse-grained description of molecular configurations wherein atomistic processes are ignored. The Fokker-Planck equation related to the kinetic theory descriptions must be solved for the distribution function in both physical and configuration spaces. When the model involves high dimensional spaces (including physical and conformation spaces and time) standard discretization techniques fail due to excessive computation requirements. In this paper, we revisit some model reduction techniques recently proposed to circumvent those difficulties, exploring other new application areas related to entangled polymer models as well as the use of such reduced models for treating complex flows in which the distribution function involves both the physical and the conformation coordinates.

Keywords

• kinetic theory
• fokker-planck equation
• model reduction
• separated representation
• karhunen-loève decomposition