How to apply CFL condition to determine time step?

[rafetsisman]

Dear all,

As far as I know, CFL condition must be considered during soil site response modelling in FEM. And this condition is considered and satisfied in OpenSEES site response analysis examples. However, the formula used in this examples is a little different than the original formula for 1D wave propagation.

Original CFL condition:
dt<=(minimum element size)/(maximum propagation velocity);

In OpenSEES examples:
dt<=(minimum element size)/(square root of maximum propagation velocity);

What is the reason for this difference? Are there any references about using the formula used in OpenSEES examples?

Thanks,

Rafet