Courant Number
 

Hi,

I am running a transient run with SSG model and monitoring the residuals.

After each timestep, the RMS & Max Courant numbers are being displayed. What is the significance of this number and what should be the range?

I am getting two tables after each time step giving the details of Locations of Maximum Residuals & Peak Values of Residuals. In the second table I am getting a loop#. What is the significance of this loop number?

For good convergance what should be the value of these numbers.

Re: Courant Number
 

The RMS & Max courant numbers are a measure of how accurate your transient calculation is. The closer the values are to 1 the more accurate the calculation will be. The values depend on the timestep you have selected, the mesh resolution and the flow velocity. If you are running at courant numbers higher than 10-20 in a transient calculation then it is likely that the calculation is not really time accurate.

Residuals (MAX/RMS) are a measure of the local control volume flow imbalances in the calculation, they basically indicate how "well solved" the problem is given the mesh, physical models and boundary conditions you have selected. Generally lower is better but getting really low values may be computationally impractical. I suggest you read through the solver modelling documentation for more details.

Neale

Re: Courant Number
 

Dear Neale,

Thank you for the prompt response and the details given by you.

In the second table, i.e., in Peak Values of Residuals, loop# is given. What is the significance of this loop number? In some of the runs, the loop# remains 1, whereas, in some other runs this number keeps changing.

For good convergence what should this loop# be?

Re: Courant Number
 

Hi Neale and Ramana,

as Neale pointed out the Courant number is a key characteristic on the errors that result from integrating the solution in time. However, as close a value to 1 is not important (except for some very simple schemes on 1-D advection equations). You want a Courant number as small as possible ie. as close to zero as reasonable.

The acceptable Cr numbers have to be determined for the problem of interest but many problems have unacceptable accuracy unless Cr is something like 0.1 or less!

Also of note is that you must have sufficient spacial resolution to resolve the features of interest. Something like 10 nodes/wave is a starting point. Then look at a Courant number of say 1 and set your time step accordingly. Do a simple problem first that has the same spacial and time scales and vary the Cr to see how it affects the accuracy.

Good Luck,

Bak_Flow

Re: Courant Number
 

Thank you Bak_Flow, for your response.