基于有限差分-谱方法的分数阶Burgers流体的非稳态驻点流动  

Unsteady stagnation point flow of fractional burgers fluid based on finite difference-spectral method

作　　者：白羽 王欣 张艳 刘春燕 BAI Yu;WANG Xin;ZHANG Yan;LIU Chun-yan(School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China;Beijing Key Laboratory of Functional Materials for Building Structure and Environment Remediation,Beijing 102616,China)

机构地区：[1]北京建筑大学理学院,北京102616 [2]建筑结构与环境修复功能材料北京市重点实验室,北京102616

出　　处：《计算力学学报》2024年第3期458-466,共9页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(21878018);北京市自然科学基金和北京市教育委员会联合资助项目(KZ201810016018);北京建筑大学青年教师科研能力提升计划(X21027)资助项目.

摘　　要：研究了分数阶Burgers流体通过拉伸平板的非稳态驻点流动问题。将分数阶导数引入Burgers流体模型可以更好地模拟流动过程,但也增加了模型的复杂性和求解难度。首次运用有限差分-谱方法求解分数阶Burgers流体模型,离散格式构造简单有效。采用谱方法对控制方程中的空间项进行离散,利用有限差分方法分别结合L-1和L-2算法离散控制方程中的时间项,给出了两种离散格式,并且通过构造数值算例证明了离散格式的收敛性。结果表明,在靠近平板处,速度随着分数阶导数的增加而减小,而无穷远处的流体速度呈现出相反的趋势,体现了分数阶导数的记忆特性。此外,雷诺数越小,流体的粘度越大,导致流体速度越大。由于松弛时间参数的松弛特性,靠近平板处松弛时间参数对速度分布有抑制作用,远离平板处松弛时间促进流体流动。Unsteady stagnation-point flow of fractional Burgers fluid towards a stretched plate was researched in this paper.Burgers fluid model introduced the fractional derivative,which could better simulate the flow process but increase complexity and solving difficulty of the model.Finite difference-spectral method solved the fractional Burgers fluid model for the first time in this paper,the discrete scheme constructed was simple and effective.Spectral method discretized space terms of the governing equations,finite difference combined with L-1 algorithm and L-2 algorithm separately discretized time terms of the governing equations,and two discrete schemes were given.Results show that velocity decreases near the plate whereas the opposite tendency appears far from plate with increment of the fractional derivative owing to the memory characteristic.In addition,a smaller Reynolds number intensifies fluid viscosity,which magnifies fluid velocity.The relaxation time parameter near the flat plate inhibits the velocity distribution and the relaxation time away from the plate promotes the fluid flow due to the relaxation characteristic.

关 键 词：非稳态 驻点流 分数阶Burgers流体 L-2算法 有限差分-谱方法 

分 类 号：O35[理学—流体力学]