# 二维非定常Navier-Stokes方程的Euler隐/显格式子格涡旋粘性非协调有限元法The Euler Implicit/Explicit Schemes with Nonconforming Finite Element Method of Subgrid Eddy Viscosity Type for the 2D Time-Dependent Navier-Stokes Equations

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In this paper, an Euler implicit/explicit scheme with nonconforming finite element method of subgrid eddy viscosity type for solving the 2D nonstationary incompressible Navier-Stokes equations under high Reynolds number  is considered. The implicit/explicit scheme which is implicit for the linear terms and explicit for the nonlinear term, avoids the severely restricted time step size from stability requirement and results in a linear system with a same constant matrix at each level of time. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation is used for the velocity and pressure field with the subgrid eddy viscosity technique, to cope with usual instabilities caused by Galerkin finite element methods. This paper also improved the restricted time step size which under stable conditions and given error estimates of velocity and pressure which independent on the viscosity .

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