Stability

The Courant condition (neglecting viscosity effects) is used to determine the stability of an ALE process.

The maximum time step is calculated by:(1)

Δ t \leq k \frac{Δ l}{c + ν - w}

Where,

The speed of sound is determined by:(2)

c = \sqrt{\frac{1}{ρ} \frac{\partial p}{\partial ρ} + \frac{4}{3} \frac{μ}{ρ}}

Where,

The relative velocity between the material and grid motion (

ν

w

) is computed by:(3)

ν - w = \sqrt{\frac{1}{N} {\sum_{i = 1}^{3} \sum_{I = 1}^{N} (ν_{i}^{I} - w_{i}^{I})}^{2}}

Where,