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二维对流扩散方程基于三角形网格的特征差分格式

王同科   

  1. 天津师范大学数学科学学院 天津 300074
  • 出版日期:2003-03-20 发布日期:2003-03-20

王同科. 二维对流扩散方程基于三角形网格的特征差分格式[J]. 数值计算与计算机应用, 2003, 24(3): 177-188.

CHARACTERISTIC DIFFERENCE SCHEMES ON TRIANGULAR MESH FOR 2D CONVECTION DIFFUSION EQUATIONS

  1. Wang Tongke (Faculty of Mathematical Science, Tianjin Normal University, Tianjin, 300074)
  • Online:2003-03-20 Published:2003-03-20
引言 对流扩散方程描述了众多的物理现象,其数值算法研究一直受到重视11一叩3一‘4].在这方面,特征差分方法和特征有限元方法是非常有效的两种方法[1一6}.特征差分方法计算简单,但适应区域不够灵活.特征有限元方法则对矩形区域或一般区域均可得到令人满意的结果,但特征有限
This paper presents two characteristic difference schemes on triangular mesh for two-dimensional linear and nonlinear convection-diffusion equations. It is proved that the two methods satisfy discrete maximum principle and they are stable in discrete maximum norm. It is also proved that they converge in discrete maximum norm and the first one has first order accuracy for convection term and the other has second order accuracy for convection term, which is especially suitable for solving strong convection-dominated diffusion problems. Finally, numerical examples show that these methods are very effective for solving convection-dominated diffusion problems.
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