On a deterministic particle-FEM discretization to micro-macro models of dilute polymeric fluids

In this paper, we proposed a deterministic particle-FEM discretization to micro-macro models of dilute polymeric fluids, which combines a finite element discretization to macroscopic fluid dynamic equation with a variational particle scheme to the microscopic Fokker-Planck equation. The discretization is constructed by a discrete energetic variational approach, and preserves the microscopic variational structure in the semi-discrete level. Numerical examples demonstrate the accuracy and robustness of the proposed numerical scheme for some special external flows with a wide range of flow rates, compared to existing stochastic simulation methods and closure approximations.