Preconditioned Multigrid Simulation of
an Axisymmetric Laminar Diffusion Flame

Samir Karaa, Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Craig C. Douglas
Center for Computational Sciences
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA


We employ a damped Newton multigrid algorithm to solve a nonlinear system arising from a finite difference discretization of an elliptic flame sheet problem. By selecting the generalized minimum residual method as the linear smoother for the multigrid algorithm, we conduct a series of numerical experiments to investigate the behavior and efficiency of the multigrid solver in solving the linearized systems, by choosing several preconditioners for the Krylov subspace method. It is shown that the overall efficiency of the damped Newton multigrid algorithm is highly related to the quality of the preconditioner chosen and the number of smoothing steps done on each level. ILU preconditioners based on the Jacobian pattern are found to be robust and provide efficient smoothing but at an expensive cost of storage. It is also demonstrated that the technique of mesh sequencing and multilevel correction scheme provides significant CPU saving for fine grid calculations by limiting the growth of the Krylov iterations.

Key words: Laminar diffusion flame, vorticity-velocity formulation, nonlinear methods, ILU preconditioning, Newton multigrid algorithm.

Mathematics Subject Classification:

Download the compressed postscript file, or the PDF file flame1.pdf.gz.
This paper has been published in Mathematical and Computer Modeling, Vol. 38, pp. 269--279 (2003).

Technical Report 359-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

This research work supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy Office of Sceince under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.