对流占优扩散方程的无网格法  

Meshless Method for Convection-dominated Diffusion Equations

作　　者：苏李君[1] 秦新强[1] 王志刚[1] 

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《武汉理工大学学报》2010年第11期172-176,共5页Journal of Wuhan University of Technology

基　　金：国家自然科学基金项目(50679073);陕西省教育厅自然科学研究项目(08JK391)

摘　　要：径向基函数配点法不需要网格划分,是一种真正的无网格方法。采用该算法的隐格式求解非定常对流扩散方程,能够消除对流占优引起的数值震荡现象。并证明了在Dirichlet边界条件下解的存在唯一性。以一维、二维对流扩散方程为例,对该算法进行了验证,并通过与特征有限元法的比较,说明该算法更具有优势。Radial basis functions collocation method is a truly meshless technique without mesh discretization.In this paper,we apply the method to the unsteady convection diffusion equations by using implicit scheme,and the method can effectively reduce the numerical oscillations.Moreover,the existence and uniqueness of the solution to the method is established under the Dirichlet boundary conditions.Numerical results are presented for 1D and 2D problems,and as compared with characteristic finite element method,this algorithm has more advantages.

关 键 词：对流扩散方程 无网格 径向基函数 配点法 

分 类 号：O241.82[理学—计算数学]