基于时滞惯性流形的非线性Galerkin算法  

IMD Based Nonlinear Galerkin Method

作　　者：侯延仁[1] 李开泰[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《应用数学和力学》2003年第3期289-299,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10101020);国家重大基础研究"973"项目(G199032801_01_5)

摘　　要：　针对Marion＿Temam型非线性Galerkin方法可行性强烈依赖于最小解题规模的不足,利用时滞惯性流形的新思想,以二维Navier＿Stokes方程为例,给出了该类非线性Galerkin方法的一种改进形式,并证明了改进后的方法在保持原方法优越性的同时,其可行性条件得到了很大的改善,从而。By taking example of the 2D Navier_Stokes equations,a kind of improved version of the nonlinear galerkin method of Marion_Temam type based on the new concept of the inertial manifold with delay(IMD) is presented,which is focused on overcoming the defect that the feasibility of the M_T type nonlinear Galerkin method heavily depended on the least solving scale.It is shown that the improved version can greatly reduce the feasible conditions as well as preserve the superiority of the former version.Therefore,the version obtained here is an applicable,high performance and stable algorithm.

关 键 词：时滞惯性流形 非线性GALERKIN算法 Marion-Temam型 NAVIER-STOKES方程 离散Gronwall引理 数值模拟 

分 类 号：O241.8[理学—计算数学] O189.33[理学—数学]