二维Navier-Stokes方程同位有限体积法的稳定性改进  

IMPROVEMENT OF THE STABILITY CONDITION OF A COLOCATED FINITE VOLUME SCHEME FOR TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS

作　　者：李旭[1,2] 伍渝江[1] 赵晓丹[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000 [2]甘肃联合大学数学与信息学院,兰州730000

出　　处：《高等学校计算数学学报》2009年第4期349-368,共20页Numerical Mathematics A Journal of Chinese Universities

基　　金：兰州大学理论物理与数学纯基础科学基金(Lzu07003);甘肃省科技计划(0804NKCA073)资助

摘　　要：1引言考虑不可压缩粘性流体的二维Navier-Stokes方程,它由速度压力公式和连续性方程的耦合组成,假设Ω是R^2的一个有界开区域,其边界为(?)Ω,对于给定的外力项f。For the numerical solution of the incompressible Navier-Stokes equations, authors such as S. Faure and R. Temam described a colocated finite volume scheme and studied its stability. Our goal in this paper is to prove new estimates on the discrete nonlinear term, to obtain two kinds of new a priori estimates on approxiraate solutions, and finally to present and prove an improved stability theorem. Theoretical and numerical results show that the new condition for stability given by us is weaker than that given by Faure et al.

关 键 词：二维NAVIER-STOKES方程 同位有限体积法 稳定性 算法 

分 类 号：O241.82[理学—计算数学]