Allen-Cahn型表面活性剂浓度的两相流格子Boltzmann模型  

Allen-Cahn-based lattice Boltzmann model for incompressible two-phase flow with surfactant

作　　者：刘紫寒 岳利清 丁兆东 LIU Zihan;YUE Liqing;DING Zhaodong(School of Economics,Wuhan Polytechnic University,Wuhan 430048,China;School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]武汉轻工大学经济学院,武汉430048 [2]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古工业大学学报（自然科学版）》2024年第3期206-212,共7页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：国家自然科学基金项目(11902165,12272188)。

摘　　要：基于相场理论,提出了含表面活性剂两相流介观格子Boltzmann(LB)模型,与经典Cahn-Hillaird型方程用于描述流体界面以及表面活性剂浓度不同,推导了Allen-Cahn(AC)型的表面活性剂浓度方程,并设计了相应的LB数值格式。该模型除了保留算法的简单性、并行性以及刻画流体组分与活性剂组分的微观相互作用外,还能准确收敛AC型宏观方程。最后利用两个算例,含表面活性剂的平板问题以及液滴问题,验证该模型准确性与稳定性。Based on the phase field theory,a mesoscopic lattice Boltzmann(LB)model for two-phase flow with surfactant is proposed.Different from the classical Cahn-Hillaird(CH)equations,which are used to describe the fluid interface and surfactant concentration,the Allen-Cahn(AC)equations are proposed in this paper,and the corresponding LB numerical schemes are designed.The model not only preserves simplicity in coding,parallelism in algorithm and capability in handling complex interface and surfactant,but also converges to the AC macroscopic equations accurately.Finally,the accuracy and stability of the model are verified by two tests,i.e.,the plate with surfactant and the droplet with surfactant.

关 键 词：表面活性剂 格子BOLTZMANN模型 Allen-Cahn型方程 

分 类 号：O24[理学—计算数学] O302[理学—数学]