Newton's method for steady and unsteady reacting flows

Shen Wensheng, Zhang Jun, Yang Fuqian

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper describes the application of Newton's method to low Mach number steady and unsteady laminar diffusion flames, which are characterized by low flow speed and highly variable density. The newly-emerged vorticity-velocity formulation of the Navier-Stokes equations is used for both steady and unsteady compressible flows to avoid staggered mesh discretization. The nonlinear Navier-Stokes equations are discretized using finite difference method, and a secondorder backward Euler scheme is applied for the time derivatives. Central difference is used for diffusion terms to achieve better accuracy, and a monotonicity-preserving upwind difference is used for convective ones. We use an unequal-sized single grid mesh for unsteady flow and a three level multigrid method for steady flow. The coupled nonlinear system is solved via the damped Newton's method for both steady and unsteady flows. The Newton Jacobian matrix is formed numerically, and the resulting linear system is ill-conditioned and is solved by the iterative solver Bi-CGSTAB with a Gauss-Seidel preconditioner.

Original languageEnglish
Title of host publicationProceedings of the 44th ACM Southeast Conference, ACMSE 2006
Number of pages2
StatePublished - 2006
Event44th Annual ACM Southeast Conference, ACMSE 2006 - Melbourne, FL, United States
Duration: Mar 10 2006Mar 12 2006

Publication series

NameProceedings of the Annual Southeast Conference


Conference44th Annual ACM Southeast Conference, ACMSE 2006
Country/TerritoryUnited States
CityMelbourne, FL


  • Diffusion flame
  • Iterative solver
  • Newton's method

ASJC Scopus subject areas

  • Engineering (all)


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