非定常不可压缩Navier-Stokes方程的特征稳定化非协调有限元方法（英文）  

Characteristic Stabilized Nonconforming Finite Element Method for the Unsteady Incompressible Navier-Stokes Equations

作　　者：荆菲菲 苏剑[1] 张晓旭[2] 刘小民[3] 

机构地区：[1]西安交通大学数学与统计学院,西安710049 [2]西北工业大学自动化学院,西安710072 [3]西安交通大学能源与动力工程学院,西安710049

出　　处：《工程数学学报》2014年第5期764-778,共15页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11001216;11371288;11272251)

摘　　要：数值求解非定常不可压缩Navier-Stokes方程的难点之一在于强烈的非线性容易引发非物理震荡,本文结合可以有效减弱此种震荡的特征线离散方法,基于局部Gauss积分之差的稳定化格式,采用最低等阶非协调混合有限元对NCP1-P1,构造出求解非定常不可压缩Navier-Stokes方程的特征稳定化非协调混合有限元方法.证明了该方法的全离散格式是无条件稳定的,并给出逼近解的相应误差估计.One of the difficulties for numerical simulation of the unsteady Navier-Stokes equa-tions is the nonlinearity, when characteristic discretization can effectively weaken the non-physical concussion caused by nonlinear form. Based on the local Gauss quadrature, this paper proposes a characteristic stabilized nonconforming finite ele-ment method to solve the unsteady incompressible Navier-Stokes equations, where the characteristic method and lowest equal-order nonconforming pair NCP1-P1 are employed. We obtain the unconditional stability of its full discrete format and the corresponding error analysis of the approximate solutions.

关 键 词：特征线方法 稳定化 非协调有限元 误差估计 NAVIER-STOKES方程 

分 类 号：O241.21[理学—计算数学] O241.82[理学—数学]