非定常N-S方程的双重网格数值模拟  

Numerical Simulation of Two-grid Method for the Unsteady Navier-Stokes Equations

作　　者：晏文璟[1] 任春风[1] 马逸尘[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2005年第6期1026-1030,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10371096).

摘　　要：本文采用全离散双重网格算法(时间变量采用Eular全隐式格式离散,空间变量采用混合有限元离散),对非定常Nayier-Stokes(N—S)方程进行数值模拟。双重网格算法的基本思想是,首先在粗网格有限元空间XH上求解一个非线性问题,然后在细网格有限元空间Xh(h《H)上求解一个线性问题。数值实验结果表明:存保持几乎相同精度的前提下,双重网格算法比标准有限元算法节省近一半的计算时间,说明了新算法求解非定常N-S方程的可行性和高效性。This paper is concerned with the numerical simulation of the unsteady Navier-Stokes equations by full discrete two-grid method （time variable is discreteized by Eular implicit difference scheme, and space variable is discreteized by mixed finite element method）. The main idea of two-grid method here is as follows： first, we solve a nonlinear equation on coarse grid finite element space X^H, then we solve a linear equation on fine grid finite element space X^h （h 〈〈 H）. The results of numerical calculation show that, given the same precision, nearly half computing time of new two-grid method can be saved when compared with the time of standard finite element method, and it is proved that this two-grid method is feasible and effective.

关 键 词：非定常N-S方程 双重网格算法 混合有限元 

分 类 号：O241.82[理学—计算数学]