发表机构
Xiangtan University（湘潭大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究开发了一种确定性 Fokker--Planck/格子-Boltzmann 微-宏求解器，用于二维稀 Hookean 聚合物溶液，通过 Hermite 系数场和双向耦合恢复宏观响应，并验证了其在多种流动中的准确性。
AI 中文摘要
聚合物溶液的确定性微-宏模拟需要构型分布函数的耦合演化与空间输运，以及将其矩转化为宏观应力并反馈至流场的处理。我们针对二维稀 Hookean 聚合物溶液中的这一耦合问题，开发了一种 Fokker--Planck/格子-Boltzmann 求解器。该求解器在无界构型空间上通过 Hermite 系数场表示分布函数，分步推进局部构型动力学与物理空间输运，并从二阶矩恢复 Kramers 应力，从而与一个纯化的双弛豫时间格子-Boltzmann 流场求解器实现双向耦合。为评估该构型描述是否能够恢复相应的宏观响应，我们以连续 Hookean 模型的精确二阶矩闭合作为宏观参考，与解析解及独立离散的宏观解进行比较。计算再现了启动 Poiseuille 流中的速度过冲和阻尼振荡，且速度剖面在网格细化下趋近解析启动瞬态；在具有空间非均匀拉伸和应力反馈的四辊流动中，在相应采样时刻和所测试的 Weissenberg 数范围内，速度与聚合物应力的全域最大相对差异分别约为 $0.0309\%$ 和 $3.84\%$。这些比较支持该求解器能够从构型分布演化中恢复 Hookean 宏观响应。进一步对壁面受限回流和开放十字槽流的计算展示了相应的构象响应以及对称和非对称流动状态，将该确定性微-宏方法推广至不同边界约束下的粘弹性流动。
英文摘要
Deterministic micro--macro simulation of polymer solutions requires the coupled evolution and spatial transport of a configuration distribution, together with the conversion of its moments into macroscopic stress and feedback to the flow. We develop a Fokker--Planck/lattice-Boltzmann solver for this coupling in two-dimensional dilute Hookean polymer solutions. The solver represents the distribution on the unbounded configuration space by Hermite coefficient fields, advances local configuration dynamics and physical-space transport in separate steps, and recovers Kramers stress from the second moment to achieve two-way coupling with a purified two-relaxation-time lattice-Boltzmann flow solver. To assess whether this configuration description recovers the corresponding macroscopic response, we use the exact second-moment closure of the continuous Hookean model as a macroscopic reference for comparison with analytical and independently discretized macroscopic solutions. The calculations reproduce velocity overshoot and damped oscillations in start-up Poiseuille flow, with velocity profiles approaching the analytical start-up transient under grid refinement; in four-roll flow with spatially nonuniform extension and stress feedback, the maximum full-domain relative differences in velocity and polymer stress are approximately $0.0309\%$ and $3.84\%$, respectively, over the tested Weissenberg numbers at corresponding sampling times. These comparisons support the solver's ability to recover the Hookean macroscopic response from configuration-distribution evolution. Further calculations of wall-bounded recirculation and open cross-slot flow exhibit the corresponding conformation responses and symmetric and asymmetric flow states, extending this deterministic micro--macro method to viscoelastic flows under different boundary constraints.
