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September 12, 1999, 12:56 
grid dependent or independent

#1 
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This may not be a question to some cfd specialists. I used Fluent code to a numerical study of the exit region of submerged laminar jets. A newtonian fluid jet is issued from a long tube into a large expanse of the same fluid. I tried many different structureed grids with different grid spacings, and I got different simulation solutions. It looks that the solution is grid dependent. In particular, when I used very dense grid, the simulation result became worse. why? I am wondering if all numerical simulations are grid dependent. If not, which case is dependent and which case is not.
Thanks for your comments. Allan 

September 12, 1999, 21:40 
Re: grid dependent or independent

#2 
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(1). To answer your first question about why the simulation result become worse when very dense mesh is used, I need to know the mesh size and arrangement used first. (2).About the second question whether all numerical simulations are grid dependent or not, I can only say that in most cases, the solutions based on coarse meshes are all mesh dependent. For your problem, there are several approaches you can take, namely,a). try other codes to solve the same problem to see whether you have the same problem, b). for the jet flow problem, you can solve the boundary layer equation to give you the answer. The boundary layer equation is much simpler to solve than the NavierStokes equations. All you need to do is to march the solution in the downstream direction, using either explicit of implicit solver for parabolic equation. c). And the last approach is to write your NavierStokes solver. (3). As to which case is mesh dependent which case is not, I would suggest that you try other sample cases first to see whether the code can produce any useful solution at all first. Then refine the mesh for that case to obtain the mesh independent solution. I sure would like to learn from you about how you are doing with the code. (I didn't use the code to solve the jet flow problem, so I can't give you any first hand information in this case.) Hope this will help.


September 15, 1999, 14:56 
Re: grid dependent or independent

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Hello Allan,
The simple truth to numerical methods is: NUMERICAL METHODS ARE ALWAYS APPROXIMATE but the approximation or numerical error can be controled and this is where the fun (money if you are the greedy type) lies! The numerical error is a function of factors like: 1. The discretization methods used ie UDS vs CDS, QUICK, limiter method, etc. and the resulting properties. 2. The grid ie. number and distribution of nodes. 3. The physical problem characteristics ie. equations being solved, domain and boundary conditions and the solution smoothness. Typically a scheme will have discretization error which is proportional to a gradient or a gradient of a gradient in the solution. So, when you say that the CFD solution appears to be grid dependant well the error being introduced is ALWAYS grid dependant and happens to be SIGNIFICANT with the grids that you are using. In the academic world you have to satisfy the criteria of the given Jounal see the ASME Journal of Fluids Engineering policy (I think that it was strongly influenced by P. Roache...correct me if I am wrong here experts!). In the real world you simply have to demonstrate that you have evaluated the numerical error and are confident that it is acceptable for the given purpose ie. planning the outlet position in your hottub: well +/ 50% will probably work but the heat shield for a reentry vehicle must be less than 1% error!!! For more info see the text by Ferziger and Peric', it has an excellent discussion of error and practial applications of CFD. Also of note is that when you are changing your grid you are changing the yplus values for wall bounded turbulent flows. Lots of stuff to think about and read! Regards................................Duane 

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