Fene Dumbbell Model And Numerical Simulation Method

The characteristics of biological macromolecules in the microscale flow has become a hot spot in microfluidic chip technology. DNA is typical of biological macromolecules. The main flow characteristics of DNA is the time-related deformation and flow pattern of DNA under different conditions in the flow field.Since 1960s, techniques of classical mechanics, molecular biological experiments and statistical analysis are combined in analyzing the rod-shaped helical structure of DNA, which obtained a lot of good results. In recent years, with the development of computer science and mathematical softwares, Brownian Dynamics Simulation is widely used as a numerical research tool in the field of rheology. Using these new tools, an effective simulation method can easily be designed for a given model.In this paper, the Brownian dynamics simulation approaches are designed to study the dynamics of DNA molecules. In our dissertation, following results are obtained:(1) We deduced the kinetic equation of FENE model with viscous and the iterative formula of Euler scheme. Then, the Euler method is introduced in simulating the dynamics of FENE model with viscous in the elongational flow. The numerical simulation results is in good agreement with Smith's experimental data.(2) The strong order-1 Milstein Derivative-free scheme is introduced to simulate the dynamics of beads-spring chain model in shear flow. We calculated the extension of moleculars and drew the mean extension distribution of molecules under different Weissenberg number. By comparing the numerical simulation results with Smith's experimental data, we got a good conclusion.(3) we derived the differential equation of the stress by the kinetic equations of the FENE model with viscosity, which can be used to study the nature of stress.