An Entropy Satisfying Finite Volume Method for the Fokker-planck Equation of Fene Dumbbell Model

In this paper, we propose a new entropy satisfying finite volume method to solve the FokkerPlanck equation of FENE dumbbell model for polymers, subject to homogeneous fluids. Both semi-discrete and fully discrete schemes satisfy all three desired properties: i) mass conservation, ii) positivity preserving, and iii) entropy satisfying. These ensure that the computed solution is a probability density, and converges to equilibrium as time evolves. Zero-flux at boundary is naturally incorporated, and boundary behavior is resolved sharply. Both one and two-dimensional numerical results are provided to demonstrate the good qualities of the scheme, as well as effects of some canonical homogeneous flows.