Connffessit-like Simulation Study On Polymer Couette Flow And Using Variance Reduction

Because of various industrial applications,theoretical and numerical studies of viscoelastic flows are of great importance today.Until recently two approaches were available:the macroscopic approach and the microscopic approach. The microscopic approach is based on the kinetic theory of liquid polymers.However due to the spirit of statistic,if we want to get the useful stastics(for example, the stress of the flows),we must simulate enough quantitative molecules and the time must be long enough.This is a great challenge for the operation ability of computer.Therefore the practicality feasible way is choose the proper kinetic simulate methods.In this way,not only can we get the main dynamic characteristic of molecules,but also we can save enough computer operation time.The CONNFFESSIT idea(Calculation of Non-Newtonian Fluid:Finite Element and Stochastic Simulation Techniques) is based on the kinetic theory of liquid polymers and focus on the dynamics of the polymer chains within the solvent,from which the stress is computed.This idea has many strongpoints:such as the constitutive equation can be disregarded,and it is easy to transform among the differents polymer models.So it has a certain degree of development prospects in the field of polymers simulation.In this paper,we present the efficient variance redction methods for CONNFFESSIT-like simulations.we simulate the frame of the Couette flow for molecule dumbbells.The main work of the paper are as follows:(1)we carefully systemicly analysed this method,and based on simulation of molecular models of polymeric fluids,the basic control equation of the Couette flow was built,and then molecule dumbbells model was added in,finally we built the control equation of the Couette flow for molecule dumbbells.(2)Based on this contral equation of the Couette flow for molecule dumbbells, we used the mathematical expectation,such as the average over an infinite number,and then combined with momentum equation of the macroscopic level,analysed these equations,wrote the corresponding simulation programe.Finally we can obtain the stress parameters and velocity parameters.(3)After Compared with the results of CONNFFESSIT method and the result which used traditional Oldroyd-B model,we used the variance reduction methods to the above method,such as the configuration fields method and contral variates method was introduced.Then we built the control equation of the CONNFFESSIT method with rariance reduction method,analysed these equations.Finally we obtained the simulation results.The results of simulation show that the noise level in the velocity and stress has been drastically reduced.The result precision has been improved,and extremely anastomose with the result which used traditional Oldroyd-B model.