Determining the time step for a transient simulation 

In this article the Courant–Friedrichs–Lewy condition (CFL condition), or Courant number criterion will be described. For the calculation of the time step, a characteristic length and the maximum velocity are required. Although the description below is for Fluent, this method can be extended to other tools. 

 

Answer 

1-The CFL condition states that the time step is given by,

Where: 

Co = Courant Number 

Δx = Characteristic length [m] 

Umax = Maximum velocity in the domain [m/s] 

 

2-Courant Number

• For explicit schemes, stability requires Co < 1 (often 0.1–0.5 is chosen for accuracy) 

• For implicit schemes, you can allow Co > 1 for stability, but accuracy usually requires Co = 0.1–1, depending on how much you want to resolve the transient scales. 

 

3-Characteristic Length

Find the smallest cell volume in your mesh (Vmin).  

In Fluent, go to Domain > Check > Perform Mesh Check 

4-Find the maximum velocity in the simulation (Umax)

• If you know the inlet velocity, be aware that the maximum velocity might be higher depending on the geometry and flow patterns. 

• Create a contour plot that includes all bodies 

• Go to the 'Results Tab' (1) > Volume integrals (2) > Select max (3) >  Select velocity (4) > Select your domain (5), and compute > The result will be shown (6) 

 

5- Example

Vmin = 1-9e-12 m3 

Δx = (Vmin)^(1/3) = 1.24e-4 m 

Vmax = 10.3 m/s 

Co = 1 

Time Step = 1.2 e-5 s