Grid Independent Solution
 

Hello all, I was wondering what is the best approach to finding a 2-D grid independent solution. When solving for a chemical reacting laminar flow and calculating the deposition of a solid product on a solid surface is it best to fix the location of the first point nearest the deposition surface and successively refine the grid from that point? Is there a better way? Any comments or suggestions would be appreciated.

Thanks, Chuck

Re: Grid Independent Solution
 

Chuck,

First off, I don't have any direct experience with deposition, but I have performed a number of grid sensitivity studies with finite-rate flow solvers. The goal for those studies was grid independent heat transfer and pressure/viscous forces. Also, let me say that I don't think the goal is to get a completely grid independent solution, but to estimate your numerical uncertainty. In general I believe that every solution solved on a grid is grid dependent. I'll also assume that you are using a structured grid. I don't know of any formalized method for performing grid independent studies on unstructured grids. Perhaps, someone else can comment on unstructured.

You have basically two parameters to vary: number of points, and grid distribution. You really need to isolate the two effects to understand the grid dependency. By grid distribution, I mean viscous spacing and grid stretching function. A good guess on required viscous spacing is for a laminar flow computation, you want your y+ at the wall to be near 1. For accurate heat transfer you may need a y+ of 0.1 to 0.01. For accurate deposition, I have no direct experience.

I would recommend the following:

1) Investigate the effect of number of points while holding the grid distribution the same. By grid distribution I mean viscous spacing and stretching function. To do this, create a very fine grid with a y+ of 1 for example. Then throw out every other point in the grid to create a grid with half the number of points. This method ensures that the coarser grid is a subset of the fine grid. This is the only way I know to completely isolate grid stretching issues. Repeat the above to create an even coarser grid. You could also refine a grid by adding points. Run a series of simulations to assess the effect of number of points. From this determine the number of points required to give you the accuracy you require. In the above process you can refine in all directions or only normal to the wall. It's your call.

2) From (1) you have determined a reasonable grid size. Now, investigate the effects of grid distribution and viscous spacing. Take your selected grid from (1) and create a new grid with viscous spacing of y+=.1. Repeat to get a grid with y+=0.01. Run a series of solutions on these grids to assess the effects of viscous spacing. Based on your experience, you may have a better idea of the y+ values to use.

From the results of 1 and 2, you should be able to estimate the uncertainty in your results. Estimating the uncertainty is all that is required for most problems. You could perform the above analysis with as little as 4 - 6 simulations, not too expensive for a 2D problem. I would be interested in your feedback on how this methodology worked for you.

Best Regards, Stacey

Re: Grid Independent Solution
 

(1). There is no fixed set of rules about how to get the grid independent solution. (2). I think, it depends on the nature of your solution. (3). My suggestion would be: plot the distribution of your solution for each varibles first, then try to determine how the function changes in space. If the solution is constant in certain region, you can use three points to cover that region. For curved function, you will need more points there. (4). Since each variable will have its own profile (solution shape), you need to combine all information to form a mesh distribution so that it will be adequate for the problem. The mesh distribution will be problem dependent and it will also depend on the treatment of your boundary conditions. (5). So, it is important to know your solution first. In this way, you will figure out where and how to distribute the grid points, and how many points are adequate for your solutions.