本文研究了求解非定常Navier—Stokes方程的稳定化分数步长法.首先,通过一阶精度的算子分裂,将非线性项和不可压缩条件分裂到两个不同的子问题中,并对非线性项采用Oseen迭代.格式分为两步:第一步求解一个线性椭圆问题;第二步求解一个广义的Stokes问题.这两个子问题关于速度都满足齐次Dilichlet边界条件.同时,在格式的第二步添加了局部稳定化项,使用等阶序对来加强数值解的稳定性.通过能量估计方法,对速度与压力做了收敛性分析和误差估计.最后,数值实验验证了方法的有效性.
In this paper, we discuss a stabilized fractional-step method for numerical solutions of the time-dependent Navier-Stokes equations. The nonlinear term and incompressible condi- tion are separated into two different sub-problems by virtue of the operator splitting method, where the nonlinear term is treated by Oseen iteration. The linear elliptic problem is solved at the first step, and the second step is to solve the generalized Stokes problem. The two problems both satisfy the homogeneous Dirichlet boundary conditions for the velocity. Furthermore, a locally stability term is added in the second step of the scheme, which enhances the numerical stability and efficiency for the equal-order pairs. The convergence analysis and error estimates for the velocity and pressure of the schemes are established via the energy method. Some num- erical results demonstrate the efficiency of the proposed method.