Burgers方程的正交基无网格Galerkin解法

Orthogonal basis meshless Galerkin method for Burgers equation

选用正交基函数作为无网格Galerkin法中的基函数,成形了正交基无网格Galerkin法.该方法克服了当基函数项数较大时方程组出现病态这一缺点,同时使矩阵计算变得简单,提高了计算效率.对Burgers方程在时间域上采用θ加权法进行离散,空间域上采用正交基无网格Galerkin法进行离散,构造了θ加权-正交基函数的无网格Galerkin法,通过对一维Bur-gers方程进行数值计算,并和现有的数值方法结果进行比较,表明了该方法的有效性.

In this paper, orthogonal basis functions were used as the basis funtions of meshless Galerkin meothod,then forming orthogonal basis function meshless Galerkin method. This method overcame the short-coming that the equations became illness when the number of the basis function was too many. At the same,this method made the matrix calculation simple and improved the calculation efficiency. To Burgers equation,the temporal was discretized by θ- weighted method,and the spatial domain was discretized by orthogonal basis function ele- ment free Galerkin method, then the θ-weighted orthogonal basis function element-free Galerkin method was constructed,one dimension Burgers equation was used to validate the algorithm, compared with existing numerical methods the results show that this method is effective.