定常Navier-Stokes方程的一个二步算法  

A Two Step Algorithm for the Stationary Navier-Stokes Equations

作　　者：陈春林[1] 王金瑞[1] 韩嘉祺[1] 黄鹏展[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2016年第23期269-273,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11401511);国家级大学生创新训练计划项目(201510755006)

摘　　要：建立了定常Navier-Stokes方程的一个二步算法.新算法第一步先基于P1-P0有限元配对求解一个非线性Navier-Stokes方程,第二步基于P2-P1有限元配对求解一个线性化Navier-Stokes方程.相比于经典的P2-P1有限元方法,方法可以使用较少的计算时间达到相同的收敛精度.数值分析和数值实验表明了算法的有效性.In this paper, we present a two step algorithm for the stationary Navier-Stokes equations. In the first step, one nonlinear Navier-Stokes problem is solved based on the P1-P0 finite element pair. Then one linearized Navier-Stokes problem is solved based on the P2-P1 finite element pair. Compared with the classical P2-P1 finite element method, the present method provides an approximate solution with same convergence accuracy. The numerical analysis and numerical experiment show that the algorithm is effective.

关 键 词：Navier—Stokes方程 有限元方法 二步算法 误差估计 数值实验 

分 类 号：O35[理学—流体力学] O302[理学—力学]