A new full discrete stabilized viscosity method for transient Navier-Stokes equations

作者：Qin, Yan mei; Feng, Min fu^*; Zhou, Tian xiao

来源：Applied Mathematics and Mechanics (English Edition ), 2009, 30(7): 839-852.

DOI：10.1007/s10483-009-0704-z

• Reynolds number
• pressure projection
• extrapolated trapezoidal rule
• transient Navier-Stokes equations

A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number (small viscosity coefficient) is proposed based oil 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 pressure projection term. Second, the artificial 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.

• 出版日期2009-7
• 单位内江师范学院