Courant Number Limit#

Courant Number Limit = <float>

Description / Usage#

This parameter’s roll is to control time step growth based on the well-known Courant number criterion. This card applies only to level-set problems. This card imposes an upper limit on the time step size, irrespective of the variable time integrator already in place.


Any floating point number to indicate the Courant number limit.


A sample card that sets the Courant number to 0.2 is:

Courant Number Limit = 0.2

Technical Discussion#

See GT-034 for a thorough discussion.


The time step limit imposed by this limit is computed as

\[\mathrm{d}t_{\mathrm{limit}} = C \min_{e} \left| \frac{h_e}{ \lVert \hat{U} \rVert_e} \right|\]

Here \(e\) is the element, \(h_e\) is the average size of the element, \(C\) is the specified Courant number, and

\[\lVert \hat{U} \rVert_e = \frac{\int_{e}^{} \delta_{\alpha} \left( \phi \right) \underline{v} \cdot \underline{n} \, d \Omega}{\int_{e}^{} \delta_{\alpha} \left( \phi \right) \, d \Omega}\]


GT-034: Tutorial on time step parameter selection for level-set problems in GOMA. April 1, 2006. D. R. Noble