摘要
传统的微分方程数值解方法求解对流占优扩散方程时,往往产生数值震荡现象,为了消除数值震荡,本文构建了一种新的数值求解方法――无网格方法进行数值求解.该方法采用配点法并引入一种新的楔形基函数构建了楔形基无网格方法,不需要网格划分,是一种真正的无网格方法,可以避免因为网格划分而影响计算效率.通过对新的楔形基函数的理论分析,证明了本文方法解的存在唯一性.最后,分别通过一维和二维的数值算例,表明该算法计算精度高,可以有效消除对流占优引起的数值震荡,是一种计算对流占优扩散方程数值解的高效方法.
Traditional numerical methods for solving convection dominated diffusion equations always cause the phenomenon of numerical oscillations. In order to eliminate the numerical oscillations, a new meshless methods is constructed in this paper. This method is based on combing the collocation method with a new ridge basis function, and always called the ridge basis meshless method. It avoids the mesh generation, and is a real meshless method. The existence and uniqueness of solutions is indicated through the theory of the new ridge basis function. Finally, two examples of one dimension and two dimension problems are presented, respectively. The numerical results show that the proposed method can effectively eliminate the numerical oscillations of convection-dominated diffusion equations. It is an efficient numerical method for convection dominated diffusion equations.
出处
《工程数学学报》
CSCD
北大核心
2013年第5期721-730,共10页
Chinese Journal of Engineering Mathematics
基金
陕西省自然科学基金(2012JM1008)~~
关键词
对流扩散方程
无网格法
楔形基函数
配点法
convection diffusion equations
meshless method
ridge basis function
collocation method
