基于SPH方法的瞬态非等温黏弹性Couette流的数值模拟  

Numerical Simulation of Transient Non⁃Isothermal Viscoelastic Couette Flows Based on the SPH Method

作　　者：许晓阳 赵雨婷 XU Xiaoyang;ZHAO Yuting(School of Computer Science and Technology,Xi’an University of Science and Technology,Xi’an 710054,P.R.China)

机构地区：[1]西安科技大学计算机科学与技术学院,西安710054

出　　处：《应用数学和力学》2023年第6期654-665,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(12071367);陕西省“特支计划”青年拔尖人才项目(289890259)。

摘　　要：基于光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)方法对瞬态非等温黏弹性流动问题进行了数值模拟.首先,模拟了等温情况下基于Oldroyd-B模型的黏弹性Couette流动;随后,将其扩展到非等温情况下进行模拟,其中选用Reynolds指数模型来评估黏度和松弛时间的温度依赖.通过与有限体积方法解的比较和对数值收敛性的评价,验证了SPH方法模拟非等温黏弹性流动问题的准确性和有效性.讨论了非等温流动相较于等温流动的不同流动特征,分析了温度依赖系数、Péclet数等对黏弹性流动过程的影响.数值结果表明,SPH方法可准确有效地模拟非等温黏弹性流动问题.Based on the smoothed particle hydrodynamics(SPH)method,the transient non⁃isothermal viscoe⁃lastic flows were numerically simulated.First,the viscoelastic Couette flow based on the Oldroyd⁃B model un⁃der isothermal condition was simulated.Then,the simulation was extended to the non⁃isothermal case,in which the Reynolds exponential model was adopted to evaluate the dependence of the viscosity and the relaxa⁃tion time on the temperature.The accuracy and effectiveness of the SPH method for simulating transient non⁃i⁃sothermal viscoelastic flows were verified through comparison with the finite volume method and evaluation of numerical convergence.The different flow characteristics of the non⁃isothermal flow compared with those of the isothermal flow were discussed.The effects of the temperature dependence coefficient and the Péclet num⁃ber on the flow physics were analyzed.The numerical results demonstrate that,the SPH method can accurately and effectively simulate transient non⁃isothermal viscoelastic flow problems.

关 键 词：光滑粒子流体动力学 非等温 黏弹性 Oldroyd-B模型 COUETTE流 

分 类 号：O242[理学—计算数学]