The Courant condition (neglecting viscosity effects) is used to determine the stability
of an ALE process.
The maximum time step is calculated by:
(1)
$$\text{\Delta}t\le k\frac{\text{\Delta}l}{c+\nu w}$$
Where,

$k$
 Coefficient
 $\text{\Delta}l$
 Smallest characteristic length of an element

$c$
 Material speed of sound
 $\nu $
 Material velocity
 $w$
 Grid velocity
The speed of sound is determined by:
(2)
$$c=\sqrt{\frac{1}{\rho}\frac{\partial p}{\partial \rho}+\frac{4}{3}\frac{\mu}{\rho}}$$
Where,

$\rho $
 Density

$\mu $
 Dynamic viscosity

$p$
 Pressure
The relative velocity between the material and grid motion (
$\nu $

$w$
) is computed by:
(3)
$$\nu w=\sqrt{\frac{1}{N}{{\displaystyle \sum _{i=1}^{3}{\displaystyle \sum _{I=1}^{N}\left({\nu}_{i}^{I}{w}_{i}^{I}\right)}}}^{2}}$$
Where,

$N$
 Number of nodes of the considered element (usually
$N$
=8)