# Stability and convergence criteria

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 September 30, 2002, 07:53 Stability and convergence criteria #1 Adriana Guest   Posts: n/a Hello, Could anyone introduce some references on convergence and stability of N-S equations for me? What's the meaning of CFL and Peclet numbers (for N-S eq.)? Thanks!

 October 1, 2002, 21:11 somebody help me !!!! #2 Adriana Guest   Posts: n/a Hello, Could anyone introduce some references on convergence and stability of N-S equations for me? What's the meaning of CFL and Peclet numbers (for N-S eq.)? Thanks!

 October 2, 2002, 01:59 Re: somebody help me !!!! #3 Tom Guest   Posts: n/a Well, there is nothing wrong with the stability and convergence of the N-S eqn. Probably you refer to stability and convergence of the numerical methods/approximations for solving the N-S equations. These issues, and CFL and Peclet numbers should be described in the basic textbooks on CFD. Perhaps you can have a look there. Tom

 October 2, 2002, 04:33 Re: somebody help me !!!! #4 Nicola Guest   Posts: n/a I suggest you to read C. Hirsch. NUMERICAL COMPUTATIONS of INTERNAL and EXTERNAL FLOWS,volume 1. John Wiley & Sons, where basic concepts of stability criteria for CFD equations are exposed. CFL (Courant, Friedrichs, Levy) number is an adimensional number used to compare temporal step and spatial step in discretized CFD equations. Peclet number is an adimensional number used to compare advection and diffusion term in energy equation. Any basic compressible fluid dynamic book could be useful for you, but you can see http://scienceworld.wolfram.com/phys...letNumber.html. Good luck

 October 2, 2002, 08:44 Ooops! #5 Nicola Guest   Posts: n/a May be Peclet number is the Peclet number of the cell and not the usual adimensional number I studied at Fluidynamics course. I apologize for the mistake. Pe=ah/D where a and D are the coefficients of the convective and diffusive term in the convection diffusion equation, h is the mesh dimension. See for reference http://www.sjc.ox.ac.uk/scr/sobey/ib...es/node10.html

 October 2, 2002, 15:39 Re: somebody help me !!!! #6 Karl Guest   Posts: n/a I suggest Versteeg and Malalasekera as an introduction to CFD basics.

 October 3, 2002, 06:08 Re: somebody help me !!!! #7 Question. Guest   Posts: n/a The Peclet number tells you the relative strength of the convection term to the diffusion term. A "large" Peclet number, say Pe>2, suggests that the convectin term dominates and will help in the choice of a suitable discretization scheme. See Versteeg as suggested by Karl.

 October 10, 2002, 20:36 Re: Stability and convergence criteria #8 Dr.Ramadan Bassiouny Guest   Posts: n/a Another comprehensive book covers this issue is " Computaional Fluid Mechanics and Heat Transfer" by Tanhill, Anderson, and Pletcher Best regards

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