基于Brown构形场的有限体积法在聚合物流动模拟中的应用

摘要

本文基于微观-宏观方法,提出了模拟聚合物流动的FVMBCF (Finite Volume Method Based on Brownian Configuration Fields)方法.为了验证该方法的有效性和计算结果的可靠性,基于Hooke哑铃模型,模拟了平面Poiseuille流动；同时,基于Hooke、FENE及FENE-P哑铃模型,模拟了突然起动的平板Couette流动,并将由FENE和FENE-P哑铃模型得到的模拟结果进行了比较分析.该方法在宏观尺度上用有限体积法求解守恒方程,微观尺度上直接从粗粒状分子模型出发,通过连续构形场的系综平均来计算应力,从而避开了需要封闭宏观方程的本构方程,也避免了追踪单个粒子轨道；该方法还具有计算效率高、稳定性强、对流项处理较简单等优点.%In this paper, the computation of polymeric flows using FVMBCF (Finite Volume Method Based on Brownian Configuration Fields) is presented based on a micro-macro approach. This method is verified and its capability is demonstrated with the planar Poiseuille flow for Hookean dumbbell models. Meantime, the time development of the planar Couette flow is studied for three molecular kinetic models with Hookean, FENE and FENE-P dumbbell models. The comparison between the FENE and FENE-P models in planar Couette start-up flows are discussed. This method couples the conservation equation at the macroscopic level with a stochastic simulation method, where the stress is computed from an ensemble of continuous configuration fields at the microscopic level based on the coarse-grained molecular models. Accordingly, this method requires neither closed-form constitutive equations nor particle tracking. In addition, this method is efficient and stable. Moreover, it is convenient to dealing with the convective term.