Convergence of Finite Element Method in Rheology
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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.Abstract: Convergence of the first-order mixed-type hyperbolic parabola partial differential equations in non-Newtonian fluid problems was studied. The coupling partial differential equations (Cauchy fluid equation, P-T/T stress equation) were used to simulate the flow zone generated by the free surface elements or excessively tensile elements. The semi-discrete finite element method was applied to solve these equations coupling with time. The finite element method 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 convergence order of the equation set reached O(h2+Δt). Numerical results of the equations were obtained through priori and posteriori error estimation of high performance computation. And the deformed sizes of the grids were presented.
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Key words:
- non-Newtonian fluid /
- semi-discrete finite element /
- coupling equations /
- convergence
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