Preconditioned multigrid simulation of an axisymmetric laminar diffusion flame

S. Karaa, Jun Zhang, C. C. Douglas

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)269-279
Number of pages11
JournalMathematical and Computer Modelling
Issue number3-4
StatePublished - Sep 5 2003

Bibliographical note

Funding Information:
This research work was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, by the U.S. Department of Energy Office of Science under Grant DEFG02-02ER45961, by the Japanese Research Organization for Information Science and Technology. and by


  • ILU preconditioning
  • Laminar diffusion flame
  • Newton multigrid algorithm
  • Nonlinear methods
  • Vorticity-velocity formulation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications


Dive into the research topics of 'Preconditioned multigrid simulation of an axisymmetric laminar diffusion flame'. Together they form a unique fingerprint.

Cite this