A Moving Grid Algorithm Based on the Deformation Method

  • Zhong Lei
  • Guojun Liao
  • Gary C. de la Pena
Conference paper


In this paper, a moving grid method based on a deformation method from differential geometry is presented. The node velocity is determined by a monitor function and a vector field which is calculated by a Poisson equation. It is proved that the cell volume is kept to be proportional to the monitor function when the grids are adapted to the solution at each time step. The moving grid method is then applied to a square cavity flow. Results show that the grid indeed follows the monitor function closely. Further research is required on constructing the monitor functions to make the method practical.


Stream Function Unsteady Flow Secondary Vortex Adaptive Grid Cavity Flow 
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  1. 1.
    J. Moser: Volume Elements of a Riemann Manifold, TVans AMS, 120, (1965).Google Scholar
  2. 2.
    G. Liao and D. Anderson: A New Approach to Grid Generation, Appl. Anal., 44, (1992).Google Scholar
  3. 3.
    G. Liao and J. Su: A Moving Grid Method for (1+1) Dimension, Appl Math Lett., 8, (1995).Google Scholar
  4. 4.
    B. Semper and G. Liao: A Moving Grid Finite Element Method using Grid Deformation, Numer. Meth. PDEs, 11, (1995).Google Scholar
  5. 5.
    P. Bochev, G. Liao, and G. dela Pena: Analysis and Computation of Adaptive Moving Grids by Deformation, Numer. Meth. PDEs, 12, (1996).Google Scholar
  6. 6.
    F. Liu, S. Ji, and G. Liao: An Adaptive Grid Method with Cell-Volume Control and its Applications to Euler Flow Calculations, SIAM J. Sci. Comput., 20, (1998).Google Scholar
  7. 7.
    G. Liao, G. dela Pena, D.A. Anderson: A Moving Finite Difference Method for Partial Differential Equations, PreprintGoogle Scholar
  8. 8.
    G. Liao, F. Liu, G. delà Pena, D Peng, and S. Osher: Level-Set-Based Deformation Methods for Adaptive Grids, J Comp Phys, 159, (2000).Google Scholar
  9. 9.
    U. Ghia, K.N. Ghia and C.T. Shin: High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method J Comp Phys, 48, (1982).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Zhong Lei
    • 2
  • Guojun Liao
    • 1
  • Gary C. de la Pena
    • 1
  1. 1.Department of MathematicsUniversity of TexasArlingtonUSA
  2. 2.VINAS Co., Ltd.OsakaJapan

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