摘要
A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number （small viscosity coefficient） is proposed based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier-Stokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. The new stabilized method is stable and has many attractive properties. First, the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pres- sure projection term. Second, the artifical viscosity parameter is added to the viscosity coefficient as a stability factor, so the system is antidiffusive. Finally, the method requires only the solution to a linear system at every time step. Stability and convergence of the method is proved. The error estimation results show that the method has a second-order accuracy, and the constant in the estimation is independent of the viscosity coefficient. The numerical results are given, which demonstrate the advantages of the method presented.
A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number （small viscosity coefficient） is proposed based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier-Stokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. The new stabilized method is stable and has many attractive properties. First, the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pres- sure projection term. Second, the artifical viscosity parameter is added to the viscosity coefficient as a stability factor, so the system is antidiffusive. Finally, the method requires only the solution to a linear system at every time step. Stability and convergence of the method is proved. The error estimation results show that the method has a second-order accuracy, and the constant in the estimation is independent of the viscosity coefficient. The numerical results are given, which demonstrate the advantages of the method presented.
基金
supported by the Sichuan Science and Technology Project (No.05GG006-006-2)
the Research Fund for Introducing Intelligence of Electronic Science and Technology of China
