CFD Online Logo CFD Online URL
Home > Forums > FLUENT

courant number

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   October 1, 2004, 02:01
Default courant number
Posts: n/a

I would like to know the relationship between the courant number and time step size.

I am trying to solve the VOF model that the liquid, surounding air, is spreading out on the surface in the closed control volume.

Please give me a tip about it.

thank you for your attention have a nice day..
  Reply With Quote

Old   October 1, 2004, 03:18
Default Re: courant number
James Date
Posts: n/a
For transient problems, it is difficult to determine the value of the time step necessary to obtain a converging solution, as the stability criteria of the complete Navier-Stokes equations cannot be found analytically. The choice of time step depends on the time scales of the important flow features which need to be resolved in the flow. Using too large a time step can often result in resolution of non-physical flow behaviour. Although from a numerical stability point of view, the time step used by implicit solvers does not have to satisfy the Courant-Friedrichs-Lewy (CFL) condition, it is often advisable for relatively small time steps close to the CFL limit to be initially used:

C = c * (dt/dx) <= 1

where C is the Courant Number, c is the speed of propagation of some important flow feature, dt is the time step and dx is the grid spacing in the direction of propagation.

Using this (CFL) criteria, an estimate of the time step needed in transient problems can be made. Based on this condition, a time step of the order of magnitude of the residence time of a fluid particle passing through a control volume is often used. The residence time, is the time it would take a fluid particle to move through a cell from one face to the opposite face. For example, if a fluid particle moves in the x-direction with a velocity u, the residence time and hence the time step necessary to capture this movement would be given by:

dt = dx/u

This calculation is typically carried out on a control volume, which is known to be located at a point with the greatest flow instability, such as the vortex street in bluff body flows. Care must, however, be taken to ensure that the time step used, is not so small that the Reynolds-averaging assumptions are violated, i.e. averaging time <= dt.
  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
IcoFoam unstability, courant number gets large! vivien OpenFOAM 10 July 23, 2013 12:48
Courant number fireman FLUENT 4 October 4, 2010 12:54
LES near wall model & courant number kasim CFX 5 March 16, 2008 19:23
IcoFoam parallel woes msrinath80 OpenFOAM Running, Solving & CFD 9 July 22, 2007 02:58
Courant number calculation - unsteady flow Kuba FLUENT 0 November 8, 2005 23:44

All times are GMT -4. The time now is 02:31.