非定常不可压Navier-Stokes方程基于欧拉格式的两水平变分多尺度方法

A Finite Element Variational Multiscale Method Based on the Backward Euler Scheme for the Time-Dependent Navier-Stokes Equations

主要研究了基于两个高斯积分的两水平全离散有限元变分多尺度方法.该方法对每个时间步长首先在粗网格上求解稳定的非线性Navier-Stokes系统,然后在细网格上求解稳定的线性问题去校正粗网格上的解.基于向后欧拉格式的时间离散推导的速度的误差估计关于时间是一阶收敛的.数值实验验证了理论的正确性和方法的有效性.

In this paper,we mainly study a fully discrete finite element variational multiscale method based on two local Gaussian integrations for the time-dependent Navier-Stokes equations.A feature of the method is that a stabilized nonlinear Navier-Stokes system is first solved on a coarse grid,and then a stabilized linear problem is solved on a fine grid to correct the coarse grid solution at each time step.Based on the backward Euler scheme for temporal discretization,we derive error bound of the approximate velocity which is first-order in time.Numerical experiments verify the correctness of the theory and the effectiveness of the method.