瞬态UCM粘弹性流体的最小二乘有限元算法  

Least-Squares Finite Element Algorithm for the Time-Dependent UCM Viscoelastic Flow

作　　者：周少玲 周锞 赵子萱 ZHOU Shaoling;ZHOU Ke;ZHAO Zixuan(School of Mathematics&Physics,Hebei University of Engineering,Handan Hebei 056038;School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工程大学数理科学与工程学院,河北邯郸056038 [2]河北工业大学理学院,天津300401

出　　处：《重庆师范大学学报（自然科学版）》2020年第4期83-89,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.61873084);河北省高等学校科学技术研究项目(No.ZD2017016);河北省省级专业学位教学案例(库)立项建设项目(No.KCJSZ2020086);河北省高等教育学会高等教育科学研究"十三五"规划课题(No.GJXH2019-100)。

摘　　要：【目的】建立求解瞬态UCM粘弹性流体的最小二乘有限元算法。【方法】利用具有一阶精度的差分格式对模型中的时间导数进行离散,得到了线性的半离散近似模型,采用最小二乘有限元方法对该近似模型进行求解。【结果】证明了最小二乘有限元解的存在唯一性,分析了最小二乘有限元解的先验误差估计,指出该估计依赖于时间步长Δt和空间步长h。通过一个三维空间的流动问题,验证了算法的有效性和收敛性。指出在实际计算中,相对于空间步长h,时间步长Δt对计算结果的影响较大。【结论】本文算法在数值精度方面,优于基于SUPG的混合有限元方法。[Purposes]A least squares finite element algorithm was presented for the time-dependent UCM viscoelastic flow.[Methods]The finite difference with first-order accuracy was used to discretize the time derivatives.The linear semidiscrete system was obtained and a weighted least squares finite element was used to solve the system.The existence and uniqueness of the numerical approximations were proved.[Findings]A priori estimate that was dependent on time step size Δt and grid sizehwas analyzed.[Conclusions]The 3D numerical results illustrated the effectiveness and the convergence of the method.It was pointed out that the errors were mainly influenced by the time step sizeΔt.The least-squares finite element method was better than the mixed finite element method based on SUPG approximation in numerical accuracy.

关 键 词：UCM粘弹性流体 瞬态问题 最小二乘 有限元方法 

分 类 号：O357.1[理学—流体力学]