## Fluids

Topics relate to Fluent, CFX, Turbogrid and more

#### Relying on Global Courant Number Larger Than Unity

• Sardar
Subscriber
Hi expert community

In the context of adaptive timestep method, Fluent uses the smallest cell dimension to calculate the global Courant number during simulation. (Please see image below, that shows console during transient calculation.)
1. Should I be committed, under any circumstances, to keeping the calculated global Courant number under unity? For example, if my Courant is 50 but my monitored field variables (average velocity, moment force etc,) reach stability by the end of every time step, is my solution reliable?

2. If the Courant number can be larger than one, can I use a representative region in my domain, instead of the minimum cell size, for determining the acceptable highest limit for my Courant number? By representative region, I mean the region that both includes an intrinsic time-varying quantity, like a rotating blade's tip speed and adjacent cell sizes, and also includes cells that are representative of the majority of cell size hoping that the solution, too, is representative of real physics of the model?
I hope I am clear.

Thanks

• Rob
Ansys Employee

If your results are converged at the end of each time step then you're probably going to get an accurate result (mesh etc assumed to be good).

Be careful with blind adherence to a number. The highest courant number could be in a region with near enough zero gradients so won't overly effect stability. Setting too high a value in the adaptive stepping may well cause you problems, too low and it'll take ages to march through time. If you're looking at updating cell position (rotating parts) if you jump cells in a time step you risk blade wake/tip effects not being picked up across the interface: courant number will be big and your result may be rubbish.

• Sardar
Subscriber

Thank you.

but I am still a bit confused, since "not jumping cells in a timestep" already means limiting Courant to less than unity in the whole simulation domain. What could be a criterion to find an optimised Courant?

• Rob
Ansys Employee

It means limiting Courant Number to under one at the interface. As cell size and velocity isn't uniform you need to take some care of what you set and define.