一种新的求解对流扩散边值问题的无网格方法

摘要

基于配点法和楔形基函数，提出了一种新的求解对流扩散边值问题的无网格方法。通过一维和二维的问题验证了该数值方法的可行性；并根据数值算例和分析，可以看到该数值方法能达到满意的收敛效果。该数值方法的隐格式形式能够有效地消除对流占优问题的数值振荡现象，是一种真正的无网格方法。%A new meshless method for convection diffusion boundary value problems is developed, which is based on the collocation method and ridge basis function. The method is applied to 1 and 2-dimensional problems to examine its appropriateness. According to numerical examples and the analysis,it is seen that the method of this paper can achieve satisfactory results. Moreover,this method can effectively reduce the numerical oscillations by using implic- it scheme of the convection diffusion problems,and is a truly meshless technique without mesh discretization.