Courant number exceeds 1

Using SimScale Fluid Flow / CFD
1

I simulate flow inside a pipe with visco-elastic material and I calculated the velocity using Bernoulli equation to assign time step in simulation control so that courant number doesn’t exceed 0.7, When I run I get “The Courant number (CFL) exceeded the limit of 1. You may experience either instability or bad temporal accuracy. It is recommended to keep the CFL number below 0.7. In order to achieve this you need to decrease the time step” . Should I use another equation to calculate velocity? Should I ignore Darcy friction Factor in Bernoulli equation? and if so, I receive a very high velocity that is not logic in results at all
Project link: https://www.simscale.com/workbench/?pid=7646801633259554377&mi=run%3A73%2Csimulation%3A61&mt=SIMULATION_RUN

2

Hi, thanks for using the forum.

How are you measuring the minimum cell size to compute the time step?

Also, perhaps you can run a test incompressible, steady state simulation to estimate the maximum speed.

3

Hello, Thank you for your response.

I’m measuring the minimum cell size from meshing set up, in my case the Minimum edge length is the minimum cell size = 0.001 m and I have to make transient simulation for studying the motion of the fluid.

I will try your advice.

4

I tried steady state simulation with 200 sec end time and got very small velocity!

Simulation Results: https://www.simscale.com/workbench/?pid=3420609661720820510&rru=1b77b0fe-e580-467f-99a8-481ee2e3835e&ci=cc2397fa-fd10-4524-ad8d-737419694e35&mt=SIMULATION_RESULT&ct=SOLUTION_FIELD

5

Hi!

Keeping the pressure difference fixed, I think that there are two things you can do to move forward:

  1. Reduce the timestep size, in proportion to your current courant number to bring it down below 1.
  2. Increase the mesh size. A coarser mesh will allow you to run an initial simulation and determine the actual flow speed more precisely.

Then you can refine the mesh accordingly until your results of interest are converged.

6

So should I increase the minimum edge length and keep the maximum as it is? or both?

7

I would say, increase the minimum length.

8

I increased the minimum edge length gradually till it reached 1 cm and still receiving the same message: “The mesh size is smaller than the cad entity tolerance or the small feature suppression tolerance for 19 faces. The mesh may be coarser than desired.”

9

Hi, this is a different error from the initial one.

Perhaps we should fork this CAD error into another topic, and keep this thread for the courant number issue.

Please also update us on the status of the courant number.

10

I ran a transient simulation on time step 0.001s and minimum edge length 3 mm and got the same result for courant number!