具有间断解的PTT型黏弹性流体热对流数值模拟  

Numerical simulation of thermal convection of PTT viscoelastic fluid with discontinuous solution

作　　者：张栏 蒋子超 陈玉惠 张仪 杨耿超 姚清河 ZHANG Lan;JIANG Zichao;CHEN Yuhui;ZHANG Yi;YANG Gengchao;YAO Qinghe(School of Aeronautics and Astronautics,Sun Yat-sen University,Shenzhen 518107,China;Robotics and Mechatronics,University of Twente,Enschede 7522 NB,the Netherlands)

机构地区：[1]中山大学航空航天学院,广东深圳518107 [2]Robotics and Mechatronics,University of Twente,Enschede 7522 NB,the Netherlands

出　　处：《中山大学学报（自然科学版）（中英文）》2023年第5期136-144,共9页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家重点研发计划(2018YFE9103900);国家自然科学基金(11972384);广东省基础与应用基础研究基金(2021B1515310001,2022B1515120009)。

摘　　要：从间断解充分发展的黏弹性流体Rayleigh-Bénard(RB)热对流具备不同流态的时间信息和发展过程的流态变换,研究该问题对阐明Phan-Thien-Tanner(PTT)型黏弹性流体RB热对流的流动机理具有重要意义。本文首次采用二阶迎风型总变差不增差分格式对PTT型黏弹性流体的RB热对流进行了数值模拟,并基于与解析解的对比论证了该数值方法在空间离散上的收敛性与二阶精度。数值结果表明,本文的数值方法可模拟自间断初始场演化的PTT型黏弹性流体RB热对流,此外,本文还对该流动发展到稳态周期解的瞬态流动现象作了基本阐释,流动现象与从先验速度场发展的流动现象一致。The study of the time information and transitional behavior of flow states in the development of intermittent solutions in Rayleigh-Bénard(RB) convection of viscoelastic fluids has great significance in understanding the flow mechanics of Phan-Thien-Tanner(PTT) viscoelastic fluid RB convection.In this paper,we first use a second-order upwind-type total variation diminishing(TVD) scheme to numerically simulate PTT viscoelastic fluid RB convection,and demonstrate the convergence and second-order accuracy of the numerical method in spatial discretization based on the comparison between the numerical and analytical solutions.The numerical results indicate that the numerical method employed in this paper can simulate the evolution of PTT viscoelastic fluid RB thermal convection with discontinuity initial field,and provide a fundamental explanation for the transient flow phenomena of this flow up to the development of steady periodic solutions,which are consistent with the flow phenomena developed from the a priori velocity field.

关 键 词：间断解 总变差不增格式 黏弹性流体 Phan-Thien-Tanner模型 Rayleigh-Bénard对流 

分 类 号：O373[理学—流体力学]