2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

AN ENTROPY SATISFYING CONSERVATIVE METHOD FOR THE FOKKER-PLANCK EQUATION OF FENE DUMBBELL MODEL

Hui Yu

Iowa State University

We propose an entropy satisfying conservative method to solve the Fokker-Planck equation of FENE dumbbell model for polymers, subject to homogeneous fluids. The first-order schemes satisfy all three desired properties: i) mass conserving, ii) positivity preserving, and iii) entropy satisfying in the sense that these schemes satisfy discrete entropy inequalities for both the physical entropy and the quadratic entropy. These ensure that the computed solution is a probability density, and the schemes are entropy stable and preserve the equilibrium solutions. Both one and two-dimensional numerical results are provided to demonstrate the good qualities of the schemes, as well as effects of some canonical homogeneous flows. We will also discuss the extension to higher order approximations in the framework of DDG (Direct Discontinuous Galerkin), with the above properties.