Deterministic particle approach of Multi Bead-Spring polymer models
Keywords:
Fokker-Planck equation, Multi Bead Spring models, method of particlesAbstract
Kinetic theory models of complex fluids involve the resolution of the advectiondiffusion Fokker-Planck equation that is usually performed using stochastic approaches. Stochastic simulation for Finitely Extensible Non Elastic (FENE) dumbbells has been successfully applied (Keunings 1997; Keunings 2004). The main difficulty found in the simulation of Multi Bead-Spring (MBS) polymer models using that approach is related to the high number of realizations required because of the highly multidimensional conformation space (Somasi et al., 2002). In a former work (Ammar and Chinesta 2005), a deterministic approach was proposed for treating the kinetic theory description of short fibers suspensions which operates by introducing the diffusion term into the advection one, then applying the method of particles. In this work, that deterministic approach will be applied to the Multi Bead-Spring polymer models in simple flows in order to conclude about its performance as well as about the impact of the conformation space dimension on the number of particles that must be considered in the simulation.
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