A method Based on Boundary Deformation for Planar Grid Generation

  • Liu, Xinru (Department of Mathematics Science and Computer Technology, Central South University) ;
  • Liu, Duanfeng (Department of Mathematics Science and Computer Technology, Central South University) ;
  • Han, Xuli (Department of Mathematics Science and Computer Technology, Central South University)
  • Published : 2009.12.31

Abstract

This paper puts forward a method based on the boundary deformation for planar grid generation. Many methods start with the special properties of grid and switch to the solution of a direct optimization or a non-linear minimum cost flow. Though with high theoretical significance, it's hard to realize due to the extremely complicated computing process. This paper brings out the automatic generation of planar grid by studying the boundary deformational properties of planar grid, which leads to uniform grid and enjoys the simplicity of computation and realization.

Keywords

References

  1. Bertsekas, D.P. (1991), Linear Network Optimization, MIT Press, Cambridge, MA
  2. Bowyer, A. (1981), Computing Dirichlet tessallations, The Comput. J, 24, 162-166 https://doi.org/10.1093/comjnl/24.2.162
  3. Castillo, J.E. and Otto, J.S. (1999), A practical guide to direct optimization for planar grid-generation, Comput. Math. Appl, 37, 123-156 https://doi.org/10.1016/S0898-1221(99)00118-2
  4. Egidi, N. and Maponi, P. (2004), A nonlinear constrained optimization problem for planar grid generation, in: Pistella, F., Spitaleri, R.M. (Eds.), MASCOTO3-3rd Meeting on Applied Scientific Computing and Tools. Grid Generation: Approximated Solutions and Visualization, IMACS Ser. Comput. Appl. Math., 8, 51-60
  5. Egidi, N. and Maponi, P. (2005), A class off network optimization methods for planar grid generation, Applied Numerical Mathematics, 52, 363-379 https://doi.org/10.1016/j.apnum.2004.08.004
  6. Lawson, C.L. (1977), Software for C1 Surface Interpolation, Mathematical Software, 161-194
  7. Peraire, J., Vahdati, P.M and Morgan, K. (1987), Adaptive remeshing for pressible flow computations, J. Computer Physics, 72, 449-466 https://doi.org/10.1016/0021-9991(87)90093-3
  8. Watson, D.F. (1981), Computing the N-dimensional Delaunay tessellation with application to Voronoi polytopes, The Comput. J, 24, 161-172 https://doi.org/10.1093/comjnl/24.2.167
  9. Watherill, N.P. (1990), Mixed structured-unstructured meshes for aerodynamic flow simulation, The Aeronauti J, 94, 111-123
  10. Zienkiewicz, O.C. and Phillips, D.V. (1971), An automatic mesh generation scheme for plane and curved surfaces by isoparametric coordinates. International Journal for Numerical Methods in Engineering, 3, 519-528 https://doi.org/10.1002/nme.1620030407