QIN Yan-mei, FENG Min-fu, ZHOU Tian-xiao. A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2009, 30(7): 783-798. doi: 10.3879/j.issn.1000-0887.2009.07.004
Citation: QIN Yan-mei, FENG Min-fu, ZHOU Tian-xiao. A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2009, 30(7): 783-798. doi: 10.3879/j.issn.1000-0887.2009.07.004

A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations

doi: 10.3879/j.issn.1000-0887.2009.07.004
  • Received Date: 2009-01-05
  • Rev Recd Date: 2009-05-18
  • Publish Date: 2009-07-15
  • A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number(small viscosity coefficient)was proposed based on pressure projection and extrapolated trapezoidal rule.The transient Navier-Stokes equations are fully-discretized by continuous equal-order finite elements in space and reduced Crank-Nicolson scheme in time.The new stabilized method is stable and has a number of attractive properties.Firstly,the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term.Secondly,the artifical viscosity parameter was added to the viscosity coefficient as a stability factor,so the system is antidiffusion.Finally,the method requires only the solution of one linear system per time step.Stability and convergence of the method was proved.The error estimation results show that the method has second order accuracy,and the constant in the estimation is independent of the viscosity coefficient.The numerical results were given,which demonstrate the advantage of the method presented.
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