[ndabir]

Hi All,

I have a rather simple though important question. I am doing an unsteady analysis of a compressible flow using coupled pressure-based solver (The reason I use pressure-base is I have to use VOF method which is not compatible with density-base solver).

My main question is how can I do a reliable mesh size and time step size independence study so that I can make sure my results will not change further significantly? Here is what I think:

1) Shall I first fix time step and refine grid. Then when the results are almost independent, refine the time step on that grid to find the desired time step?

2) Or shall I use a fix CFL number for the flow (such as 0.25), and based on CFL= velocity of sound*dt/dx and a grid size (dx), find the time step and do a simulation. Then by keeping CFL the same (0.25), half the grid size (therefore the time step should be half) and do another simulation and compare the results?

Is there another method too?
Are both the 1st and 2nd methods I mentioned above correct?

[ndabir]

Let me make my question more clear:

How do you guys usually do grid and time step size study for an unsteady flow?
what is the correct procedure for that?

[LuckyTran]

Originally Posted by ndabir

Hi All,

I have a rather simple though important question. I am doing an unsteady analysis of a compressible flow using coupled pressure-based solver (The reason I use pressure-base is I have to use VOF method which is not compatible with density-base solver).

My main question is how can I do a reliable mesh size and time step size independence study so that I can make sure my results will not change further significantly? Here is what I think:

1) Shall I first fix time step and refine grid. Then when the results are almost independent, refine the time step on that grid to find the desired time step?

2) Or shall I use a fix CFL number for the flow (such as 0.25), and based on CFL= velocity of sound*dt/dx and a grid size (dx), find the time step and do a simulation. Then by keeping CFL the same (0.25), half the grid size (therefore the time step should be half) and do another simulation and compare the results?

Is there another method too?
Are both the 1st and 2nd methods I mentioned above correct?

Both these methods are correct. However there is a third way similar to 1). I'm going to call it 1b.

1a) Fix the time-step, refine the grid.
1b) Fix the grid, refine the time-step. That is, half the time-step on your original grid.
2) refine both grid and time-step, keeping Courant number the same

1a) allows you to quantify the grid sensitivity
1b) allows you to quantify the time-step sensitivity
2) allows you to quantify both

Unless you are specifically interested in what is the grid's contribution and what is the time-step contribution to your sensitivity, you do not need to do 1a & 1b. Hence, I always do 2. 2) captures both grid and time-step sensitivity, but does not allow you to distinguish how much sensitivity came from where. If you just want overall sensitivity, doing 2) is sufficient.

[ndabir]

Thanks LuckyTran for your reply.

Is there a way to find what courant number should be used in method 2?
I am using 0.25 but if you have a high speed computer I think the smaller the courant number, the better the result. What is your idea?

Is it reasonable (or do people usually do it) to compare several courant numbers together such as 0.75, 0.5, 0.25 and report the results based on that?or you can just pick a arbitrary courant number and do the grid and time step study?

[LuckyTran]

Originally Posted by ndabir

Thanks LuckyTran for your reply.

Is there a way to find what courant number should be used in method 2?
I am using 0.25 but if you have a high speed computer I think the smaller the courant number, the better the result. What is your idea?

Is it reasonable (or do people usually do it) to compare several courant numbers together such as 0.75, 0.5, 0.25 and report the results based on that?or you can just pick a arbitrary courant number and do the grid and time step study?

Courant number is not very useful in this regard. Think of the example of 1b). The Courant number sensitivity is already determined from that test. So going to 2) should also capture the same effects. But by halving the grid size, you halved the Courant number even though your time-step is obviously superior than before.

What is truly important in transient/unsteady simulations is the time-step size relative to the time-scale of the phenomenon. Unfortunately Courant number entangles that with an arbitrary length scale. That is, Courant number is more closely related to a length scale (the grid size) than the characteristic time-scales of the flow.