A fast solver for Fokker–Planck equation applied to viscoelastic flows calculations: 2D FENE model

In this paper, we introduce a new method for solving efficiently the Fokker–Planck equation arising in the simulation of dilute polymeric solutions. For a two-dimensional FENE (Finitely Extensible Nonlinear Elastic) model, the structure of the Fokker–Planck equation is used to design a fast solver. The resulting equations are discretized with a spectral/spectral element method. Application of the method to flow of a FENE fluid past a confined cylinder demonstrates readily the advantages of the proposed scheme over traditional stochastic simulations.