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工程力学  2013 

采用不同插值函数的流体力学有限元数值波动研究

DOI: 10.6052/j.issn.1000-4750.2012.07.0522, PP. 266-271

Keywords: 对流扩散方程,流体力学有限元,数值波动,插值函数,指数型插值函数

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Abstract:

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。

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