[majidsvn7]

Hi all,
I understand the concept of grid independence of solution, but I am confused about recognizing a few issues:
suppose we are going to modeling turbulence pipe flow,
1.To follow independency of the grid, variation of which parameter against which variable should be plotted?!!!
for instance, Is the radial velocity distribution in the pipe suitable for different grid sizes?
2. how to determine what size of grid is the coarse mesh and fine mesh for a specific problem such a pipe? for instance, I wanna begin with 100*30 , is this a coarse mesh and refining this mesh means changing it to 200*60?!!!
3.When we're going to run a case after refining the mesh, all the control parameters such as timestep, end time and ... should be the same in coarse mesh and finer mesh or not ?!

[LuckyTran]

Grid (in)dependence is a concept and artform, not an exact science.



1. It's up to you. Your objective for running the CFD might not be the same as everyone else's. One person might want every velocity in every cell to be mesh independent, but another might only want the velocity at the centerline. Yet another person might only care about the bulk average velocity.
2. Experience goes a long ways here. Start with order of magnitude and work your way from there. If you start with 100*30, in principle, you should half the cell size in each direction and go to 200*60 (or by an entire decade even and go to 1000*300). Doubling is not enough to see order of convergence, even though that's a general rule of thumb, you really need decades. In practice, few people can afford massive grids and they like to use results from the finest grid anyway, so it is much more common to see grid refinements like 120*32 as the next step. If you can, go for it (the 200*60).

3. Generally, settings should be the same if you only want to see mesh sensitivity (and not setting sensitivity). For transient simulations it gets a little wonky because the Courant number (which is a non-dimensional time-step size) is directly grid dependent and time-step independent. You can do a separate or combined time-step size (in)dependence study the same way you would do a grid study.

[sbaffini]

I would add that:

2) If you don't actually see a grid convergence on the chosen grids (but you are sure the code is correct), then probably you started too coarse

3) If you don't keep a constant Courant in unsteady cases, which means reducing the time step as well, you might soon hit the time step accuracy barrier and see no further error reduction

[FMDenaro]

I would say that the concept of grid independent solution is somehow weak and a well assessed framework does depend on the flow problem.
The "theoretical" case assumes you have an ideal exact solution and grid convergence should drive to a convergence towards an exact solution.
But in practical engineering problems you don't have an exact solution so what does grid-independent solution really mean? It should identify only a solution where you suppose that the local truncation error tends to vanish and what you get is only a result of the adopted approximate physical model. Using such approach in RANS/URANS means you have a convergence toward the turbulence model-governed solution. This way you should check the whole fields, for example extracting the values of the variables on same nodes available for all the refined grids and evaluating if the variations are small in some norms. I do not think that integral quantities have a real meaning in this analysis, you need to check the real computed variable.
As already addressed above, grid convergence study requires to work at constant CFL number to have a correct meaning.

[majidsvn7]

Originally Posted by LuckyTran

Grid (in)dependence is a concept and artform, not an exact science.



1. It's up to you. Your objective for running the CFD might not be the same as everyone else's. One person might want every velocity in every cell to be mesh independent, but another might only want the velocity at the centerline. Yet another person might only care about the bulk average velocity.
2. Experience goes a long ways here. Start with order of magnitude and work your way from there. If you start with 100*30, in principle, you should half the cell size in each direction and go to 200*60 (or by an entire decade even and go to 1000*300). Doubling is not enough to see order of convergence, even though that's a general rule of thumb, you really need decades. In practice, few people can afford massive grids and they like to use results from the finest grid anyway, so it is much more common to see grid refinements like 120*32 as the next step. If you can, go for it (the 200*60).

3. Generally, settings should be the same if you only want to see mesh sensitivity (and not setting sensitivity). For transient simulations it gets a little wonky because the Courant number (which is a non-dimensional time-step size) is directly grid dependent and time-step independent. You can do a separate or combined time-step size (in)dependence study the same way you would do a grid study.

Thank you. This is exactly what I needed. I got it.

[majidsvn7]

Originally Posted by FMDenaro

I would say that the concept of grid independent solution is somehow weak and a well assessed framework does depend on the flow problem.
The "theoretical" case assumes you have an ideal exact solution and grid convergence should drive to a convergence towards an exact solution.
But in practical engineering problems you don't have an exact solution so what does grid-independent solution really mean? It should identify only a solution where you suppose that the local truncation error tends to vanish and what you get is only a result of the adopted approximate physical model. Using such approach in RANS/URANS means you have a convergence toward the turbulence model-governed solution. This way you should check the whole fields, for example extracting the values of the variables on same nodes available for all the refined grids and evaluating if the variations are small in some norms. I do not think that integral quantities have a real meaning in this analysis, you need to check the real computed variable.
As already addressed above, grid convergence study requires to work at constant CFL number to have a correct meaning.

Thanks. It is an interesting and reflective answer

[Jonas Holdeman]

I would think that grid-independence would include solutions that are invariant under perturbations that rotate, translate, skew, and scale the grid.