Volume 42 Issue 2
Feb.  2021
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QIU Zhouhua, ZENG Zhong, LIU Hao. A PN×PN-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289
Citation: QIU Zhouhua, ZENG Zhong, LIU Hao. A PN×PN-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289

A PN×PN-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations

doi: 10.21656/1000-0887.410289
  • Received Date: 2020-09-24
  • Rev Recd Date: 2020-10-12
  • Publish Date: 2021-02-01
  • A PN×PN-2 spectral element method based on the Picard linearized iteration was presented for the solution of 2D steady incompressible Navier-Stokes equations. Through the Picard iteration, the Navier-Stokes equations were converted to a series of Stokes-type equations to be solved with the PN×PN-2 spectral element method on the non-staggered grid in each iteration step. In order to eliminate the pseudo pressure mode, the pressure discretization is 2 orders lower than the velocity discretization, and the application of non-staggered grids makes the discretization of the equation convenient and avoids the interpolation error. The Stokes flow, the Kovasznay flow and the lid-driven cavity flow were simulated with the present method. The numerical results show that, the error converges with the spectral accuracy. In addition, avoidance of the pressure oscillation phenomenon indicates the accuracy and reliability of the present method.
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