Generating elliptic grids in three dimensions by a method of false transients

Authors

  • Eddie Ly
  • Daniel Norrison

DOI:

https://doi.org/10.21914/anziamj.v49i0.313

Abstract

A finite difference method based scheme incorporating a method of false transients and an approximate factorisation technique is presented for solution of a system of Poisson's equations used for grid generation. A time step cycling process with repeated endpoints is incorporated into the scheme to enhance the convergence rate. The scheme required much less computational effort than all other numerical schemes compared in this article, to obtain a high quality grid over a body (converged solution) in three dimensions. Although, the superiority of the scheme has been demonstrated for a grid generation problem, it may be applied for other problems requiring the numerical solution of a set of similar partial differential equations. References
  • Ly, E., and Gear, J. A., Time-Linearized Transonic Computations Including Shock Wave Motion Effects, Journal of Aircraft, 39, 6, Nov-Dec 2002, pp. 964--972.
  • Ly, E., and Nakamichi, J., Time-Linearised Transonic Computations Including Entropy, Vorticity and Shock Wave Motion Effects, The Aeronautical Journal, Nov. 2003, pp. 687--695.
  • Ly, E., and Norrison, D., Automatic Elliptic Grid Generation by an Approximate Factorisation Algorithm, ANZIAM Journal, 48 (CTAC2006), pp. C188--C202, July 2007.
  • Mathur, J. S., and Chakrabartty, S. K., An Approximate Factorization Scheme for Elliptic Grid Generation with Control Functions, Numerical Methods for Partial Differential Equations, 10, 6, 1994, pp. 703--713.
  • Thompson, J. F., Thames, F. C., and Mastin, C. W., Boundary-Fitted Curvilinear Coordinate Systems for Solution of Partial Differential Equations on Fields Containing any Number of Arbitrary Two-Dimensional Bodies, NASA Contractor Report CR-2729, Washington DC, USA, July 1977, 253 pages.
  • Warming, R. F., and Beam, R. M., On the Construction and Application of Implicit Factored Schemes for Conservation Laws, in SIAM-AMS Proceedings, 11, USA, 1978, pp. 85--129.
  • Catherall, D., Optimum Approximate-Factorization Schemes for Two-Dimensional Steady Potential Flows, AIAA Journal, 20, 8, 1982, pp. 1057--1063.
  • Gear, J. A., Time Marching Approximate Factorization Algorithm for the Modified Transonic Small Disturbance Equation, Research Report Number 6, Department of Mathematics, RMIT University, Melbourne, Australia, Feb. 1996, 11 pages.
  • Hoffmann, K. A., Computational Fluid Dynamics for Engineers, Engineering Educational System, Texas, USA, 1989.
  • Ly, E., Improved Approximate Factorisation Algorithm for the Steady Subsonic and Transonic Flow over an Aircraft Wing, in Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS98), AIAA and ICAS, Melbourne, Australia, Sep. 1998, Paper A98-31699.

Published

2007-11-07

Issue

Section

Proceedings Engineering Mathematics and Applications Conference