采用不同插值函数的流体力学有限元数值波动研究

NUMERICAL WAVE OF FINITE ELEMENT SOLUTION IN FLUID MECHANICS USING DIFFERENT INTERPOLATION FUNCTIONS

对一维定常对流扩散方程有限元解的波动问题进行汇总和分析,讨论产生有限元解波动的原因,介绍常用的处理解波动的基本原理和技术。采用不同插值函数进行有限元分析,并与解析解对比,重点讨论了指数型插值函数有限元解的波动和收敛性。研究结果表明提高插值函数连续性可以改善一维对流扩散方程有限元数值波动情况。与线性Lagrange插值函数相比,指数型插值函数可精确给出变量在单元内的分布,并能较好地控制数值波动现象。同时在较稀疏的网格条件下,指数型插值函数可取得问题较好的数值解。

The finite element solution of one dimensional stationary convection diffusion equation for wave problems is summarized and analyzed. The reasons for wave are discussed and the basic principles and techniques which deal with the wave are also displayed. By using different interpolation functions, the results of finite element solutions are compared with that of the analytical solution. The wave and convergence of a finite element solution using an exponential function based interpolation （EFBI） are focally analyzed. The results show that the continuity improvement of interpolation functions can decrease the wave degree. Compared with the liner Lagrange interpolation function, an EFBI function can simulate the distribution of variables within the unit accurately and is effective to deal with the problem of numerical waves. In the condition of sparse grids, the finite element method using an EFBI function has a good solution.