非定常Navier-Stokes方程有限元算子分裂算法

The Finite Element Operator Splitting Method for the Incompressible Navier-Stokes Equations

在连续解的正则性假设条件下,基于亚格子稳定模型和算子分裂方法提出了非定常不可压Navier-Stokes方程的有限元算子分裂算法.其主要思想是:利用算子分裂方法把非线性项和不可压缩项分开,首先求解一个线性化的Burger's问题得到有限元解■,然后再求解一个Stokes问题得到解u■.证明了速度的误差估计关于时间是一阶收敛的,并给出数值实验验证了理论的正确性.

Under the regularity assumptions on the continuous solution, we provide a finite element operator splitting method for the simulation of unsteady incompressible Navier-Stokes equations, which is based on the subgrid model. It is a two-step scheme in which the nonlinearity and incompressibility are split into different steps. First, a linear Burger’s system is solved, and the solution of the finite element uh^n+1/2 is obtained. Then a Stokes problem is solved, and its solution uh^n+1 is obtained. We derive the error bound of the approximate velocity which is first-order in time. Numerical experiments have verified the correctness of the theoretical analysis.