流变计算的高性能有限元收敛性分析  

Convergence of Finite Element Method in Rheology

作　　者：侯磊[1,2] 孙先艳[1] 赵俊杰[1] 李涵灵[1] 

机构地区：[1]上海大学理学院数学系,上海200444 [2]上海交通大学上海高校计算科学E-研究院,上海200030

出　　处：《应用数学和力学》2014年第4期412-422,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11271247)~~

摘　　要：文中研究非Newton(牛顿)流体流变问题的混合型双曲抛物一阶偏微分方程的收敛性,采用耦合的偏微分方程组(Cauchy流体方程、P-T/T应力方程),模拟自由表面元或由过度拉伸元素产生的流域.使用半离散有限元方法进行求解,对于含有时间变量的耦合方程,在空间上用有限元法,利用三线性泛函来解决偏微分方程组的非线性;在时间上用Euler(欧拉)格式,得出方程组的收敛精度可达到O(h2+Δt).通过高性能计算的预估计和后估计得到方程的数值结果,并显示网格变形的大小.Convergence of the first-order mixed-type hyperbolic parabola partial differential e- quations in non-Newtonian fluid problems was studied. The coupling partial differential equa- tions （Cauchy fluid equation, P-T/T stress equation） were used to simulate the flow zone gen- erated by the free surface elements or excessively tensile elements. The semi-discrete finite ele- ment method was applied to solve these equations coupling with time. The finite element meth- od was used in space. The trilinear functional was employed to solve the nonlinear problems of partial differential equations. In the time domain the Euler scheme was adopted. The conver- gence order of the equation set reached O（ h2 ＋ At） . Numerical results of the equations were ob- tained through priori and posteriori error estimation of high performance computation. And the deformed sizes of the grids were presented.

关 键 词：非Newton流体 半离散有限元 耦合方程 收敛 

分 类 号：O357.1[理学—流体力学]