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A compact streamfunction-velocity scheme for the 2D unsteady incompressible Navier-Stokes equations in arbitrary curvilinear coordinates

  • Jian-xin Qiu (仇建新)
  • Bo Peng (彭博)
  • Zhen-fu Tian (田振夫)Email author
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Abstract

A streamfunction-velocity formulation-based compact difference method is suggested for solving the unsteady incompressible Navier-Stokes equations in the arbitrary curvilinear coordinates, in which the streamfunction and its first derivatives as the unknown variables are utilized. Numerical examples, involving the boundary layer problem, a constricted channel flow, driven polar cavity flow and trapezoidal cavity flow problem, are solved by the present method. Numerical results demonstrate the accuracy of the currently proposed scheme and exhibit the numerical capability to simulate the flow problems on geometries beyond rectangular. For driven polar cavity flow problem, the results show that the flow phenomena for Re = 5000 is not steady rather time-periodic, and the critical Reynold number (Rec) for the occurrence of a Hopf bifurcation is given.

Key words

Streamfunction-velocity formulation arbitrary curvilinear coordinates compact scheme unsteady incompressible flow 

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Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Jian-xin Qiu (仇建新)
    • 1
  • Bo Peng (彭博)
    • 1
  • Zhen-fu Tian (田振夫)
    • 1
    Email author
  1. 1.Department of Mechanics and Engineering ScienceFudan UniversityShanghaiChina

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