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

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.