Courant  Number in explicit formulation

The Courant number is a mathematical condition named after Kurt Friedrichs, Hans Lewy and Richard Courant. Moreover, they came up with an equation that measures the stability of convergence which is essential for any successful numerical simulation.

The equation is simple to apply at each element and time step. In addition, it can be applied in 1, 2 or 3 dimensions.

The equation involves the spatial coordinate, time and velocity :

formula in one dimension
formula in one dimension

For a 2 dimensional problem:

Courant number for 2 dimensional problem
Courant number for 2-dimensional problem

The conditions above apply to numerical solutions in the explicit form. Also, Fluent ANSYS calculates the CFL number which is usually displayed in the command window when using the VOF model in the explicit formulation. Another reason to use a smaller time step is to make sure to meet the conditions set by the formulas above. Beside that, the CFL number is different when using the implicit formulation.

To watch the video, please click this link: Youtube Video. Also, please don’t forget to subscribe to my channel. 

You can download the geometry created for this tutorial and try to create your own simulation. Furthermore, the 3D container model consitutes 2 inlets and 1 outlet. The height of the container is approximately 0.9m.

Use the K-Epsilon model and apply the scalable wall function when the inflation layers are too close to the wall. 

Please click on the following link to download the 3D geometry


VOF multiphase model
VOF multiphase model
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