[wzhang11]

Hi all

I have a puzzle about grid independent study for the transient simulation, I was told to use 2 times of cell number to conduct simulation, but I am not sure should I keep the Courant Number or timestep size constant for different mesh size, e.g. I want Courant Number equal to 1 then I need to change timestep everytime according to courant number definition.
can anyone give me some ideas?

Cheers
Jason

[LuckyTran]

For a sensitivity study, you should also reduce time-step size.

You are trying to quantify the spatial AND temporal discretization effect. You can do this separately or combined.

Reducing cell size lets you study spatial discretization. Reducing time-step size lets you study temporal discretization.

If you reduce the grid size and keep the same time-step that answers only the spatial discretization (the grid dependence) but does not give you any information on the time-step dependence.

You can also reduce time-step size and keep the same grid (time-step dependence but not grid dependence). Or you can reduce both the grid size and time-step size at the same time. You won't be able to isolate which influences the solution more (grid or time-step) but you'll know their combined influence.

[wzhang11]

Hi Lucky

Thanks for your help, maybe my question is very clear. Actually I want to know when I study grid independent, should I keep a constant timestep, as you know, the courant number = velocity*timesetp/smallest cell size, thus the courant number will change according to different mesh size. therefore, I feel confused what should I to make a balance between Courant Number and Timestep. So far, what I do is trying to monitored the CFL number through report regrading to different timestep for a reasonable mesh zize, then pick a timestep size which can ensure Courant number is below or below 1. after this, I will start the grid independent study. But I am not sure am I right.

Cheers
Jason

[LuckyTran]

That is on the right track.

But once you get to the grid dependence study, you may choose to keep the same time-step and get a different Courant number or a smaller time-step and get the same Courant number. You should do the latter to capture both spatial and temporal effects.

[wzhang11]

Originally Posted by LuckyTran

a smaller time-step and get the same Courant number. You should do the latter to capture both spatial and temporal effects.

Hi Lucky

Thanks for your advice, did you mean for a finer mesh, I still need to change timestep to achieve same Courant number or I use a smaller Timestep for all mesh size to ensure the Courant Number is within certain range like '0~0.5'.

Cheers
Jason

[LuckyTran]

Originally Posted by wzhang11

Hi Lucky

Thanks for your advice, did you mean for a finer mesh, I still need to change timestep to achieve same Courant number or I use a smaller Timestep for all mesh size to ensure the Courant Number is within certain range like '0~0.5'.

Cheers
Jason

Both. You need some grid size and some time step to do whatever it is you want to do. If you want Courant No 0-0.5 then of course you need a small enough time-step. But now suppose you have a simulation setup with some grid size dx and some time-step dt.

Then you need to make the mesh finer/coarser for your grid convergence study. When you do the grid convergence study you should vary both dx and dt.