In complex numerical models having mesh elements nearing a million, its highly impossible for GIT due to time and constraints. So is GIT necessary or is there any alternate option?
The answer depends on the use of the model.
If it is desired to generate numerical results simply to demonstrate the graphical capabilities of the tool, then grid dependence is not a liability. In other words, if the model results are of little or no consequence, then prediction accuracy is not an objective, and grid independence is not required.
If, on the other hand, the prediction's degree of accuracy must be known because the prediction will drive a consequential decision, then grid independence is required. (With grid independence, the analyst might be able to estimate the inaccuracy of the prediction. Grid dependence may preclude any estimation of that inaccuracy.)
Unfortunately, model complexity seduces analysts into the assumption that grid-dependent model results are adequate (accurate enough), perhaps because they are plausible. Sadly, many consequential decisions are based on complex model results advertised as "valid" despite having little or no insight into the degree of real-world accuracy (i.e., inaccuracy).
Perhaps most challenging: unlike academic exercises, real-world applications tend to be so complex that grid independence is not realistically achievable. That leaves the analyst in a predicament: can he/she be candid about the modeling limitations? Should a consequential decision be based on computational model predictions of unknown accuracy?
My advice: Grid-dependent results are unavoidable for many real-world applications; however, they should never be accompanied by deceptive labels such as "accurate" or "valid" or "physics-based." Grid-dependent models are simply an engineering tradeoff that may provide some insight into the dynamics of the complex system. They may be more useful as motivators for advanced testing of complex systems.
GIT is always recommended because it is possible that the result you are getting is not up to the mark. Also GIT justifies your meshing as well as it may reduce your simulation time.
Dear colleague
As you know in large scale CFD problems, computation cost is crucial and even you can not finer your mesh due to your hardware so GIT test may bother you!
you may finer your mesh in critical points:
1-if your approach is Eulerian-Eulerian , the cells of highest velocity stream
2-if your approach is VOF, in interface of phases
3- if your looking to problem is DPM in path of partices
and so on.
then you may analyze error, and clarify your mesh performance.
in this way you may not suffer from higher cost of Computation
regards
Hi! This problem can be avoided if you can estimate the minimum size of the inhomogeneity of the expected solution.
I choose the cell size ten/twenty times less than the size of the inhomogeneity.
The code itself should certainly be tested for grid independency, using well-established test-cases. That does not mean you should test every simulation you run. Obviously time constraints will get in the way for large models. Also, certain simulations need a specific grid-typ in order to be possible at all due to dimension and symmetry issues.
The answer depends on the use of the model.
If it is desired to generate numerical results simply to demonstrate the graphical capabilities of the tool, then grid dependence is not a liability. In other words, if the model results are of little or no consequence, then prediction accuracy is not an objective, and grid independence is not required.
If, on the other hand, the prediction's degree of accuracy must be known because the prediction will drive a consequential decision, then grid independence is required. (With grid independence, the analyst might be able to estimate the inaccuracy of the prediction. Grid dependence may preclude any estimation of that inaccuracy.)
Unfortunately, model complexity seduces analysts into the assumption that grid-dependent model results are adequate (accurate enough), perhaps because they are plausible. Sadly, many consequential decisions are based on complex model results advertised as "valid" despite having little or no insight into the degree of real-world accuracy (i.e., inaccuracy).
Perhaps most challenging: unlike academic exercises, real-world applications tend to be so complex that grid independence is not realistically achievable. That leaves the analyst in a predicament: can he/she be candid about the modeling limitations? Should a consequential decision be based on computational model predictions of unknown accuracy?
My advice: Grid-dependent results are unavoidable for many real-world applications; however, they should never be accompanied by deceptive labels such as "accurate" or "valid" or "physics-based." Grid-dependent models are simply an engineering tradeoff that may provide some insight into the dynamics of the complex system. They may be more useful as motivators for advanced testing of complex systems.
GIT only speaks about round-off errors based on no. of cells used.Further, grid quality and proper resolution of key areas are going to affect CFD prediction.
All of the answers above are great, and all necessary. The problem is always that the order of convergence is never really known, nor whether the solution is monotonically converging or oscillating around a solution.
Having said that, I will always get some form of rigorous GIT completely, at the very least it shows you the sensitivity to grid refinement around the area of realisable solutions.
Yes it is must. Try to strat with a coarser mesh and once u r happy with solution then refine the mesh and run ur case and get convergence
Grid study independency is an indispensable part of every numerical simulation in the domain of CFD; to reduce the computational cost, you should start with coarser mesh and gradually make it fine util your solution becomes independent of the number of grids.
Dear All - Thanks for all your inputs.
But my model is a shell-and-tube type heat exchanger with about 25 tubes. For proper simulation, it needs about a million elements. If I reduce the number of elements, some boundaries are not meshed properly. In this case, GIT is very tough for me. Need all your kind inputs.
Your objective is "proper simulation" but it is not clear what you intend as "proper."
If you simply want to create a computational model that provides plausible stresses and strains, yet no consequential decisions will be based on the computations, then a proper simulation can be very simple and straightforward. No significant effort is required to demonstrate that the simulation represents reality with any degree of accuracy.
If, on the other hand, simple plausibility is insufficient because consequential decisions will be based on the computational predictions, then you will need to demonstrate the degree of accuracy of the intended predictions. That is exceedingly difficult for typically complex models of real-world systems. (It is difficult enough for idealized/simplistic examples employed in academic settings.) After all, you probably need to anticipate stress concentrations, weld effects, material discontinuities, etc.
Given those challenges, you will likely be unable to demonstrate the degree of real-world accuracy of the intended predictions. But you may be able to demonstrate that your computational model accurately represents your idealized "conceptual model" of reality. (In other words, recognize that your computational model only approximates reality under highly idealized conditions; you have introduced many modeling approximations and shortcuts that should not be ignored.) If you do not demonstrate grid convergence, then you cannot even claim to accurately represent that highly idealized reality.
In effect, lack of grid convergence introduces yet another level of abstraction/approximation into the computational model. Yet it may still be a "proper simulation" if you can tolerate unknown predictive accuracy.
"Reality bites."
Dear Hans U. Mair - Thanks for the inputs. Sorry that I have not given much information earlier. Actually my simulation is a highly non linear problem which necessitates relatively finer mesh. There are three elements/materials - inside tube (fluid), copper tube and outside tube. I have tried eliminating copper tube by a conductive layer which results in the reduction of mesh elements - but the results are far from reality. I got good results with a single tube model having copper tube which matches with an experimental data (5% error - acceptable).
1. there is always grid dependency, especially for unstructured grid methods.
2. in order to prove the order of your method u need of course to solve for the analytical solution on different grids, write L2-Norms on a double log scale and the gradient is the order of the scheme.
3. unstructured grids are often oriented in such a ways that cross flow diffusion is reduced, this is very dangerous since the solution depends on your grid, arbritrary distribution of elements is more appreciated but for some applications it makes very high order methods needed and then it is often not effordable so a compromise is to adopt the grid in a certain sense to the solution (a priori error estiamtes).
•Numerical errors.
–Solving equations on a computer invariably introduces numerical errors.
–Round-off error: due to representation of numbers with a finite number of digits (significant digits).
–Truncation error: due to approximations in the numerical models.
the mesh refinement is very useful. Using experimental data for simple case will help to select the mesh
GIS is needed to show that your results are the same irrespective of mesh, however for large models you can refine your mesh without doubling it.
you can refine your mesh locally in zones of interest especially zones with high gradient.
you can check my test case in this link
Article Control of Leakage Flow by Triple Squealer Configuration in ...
Dear Hakeem Niyas,
are you familiar with the concept of 'a posteriori error estimators'?
They are local, cell based quantities that can be calculated from the computed solution and the data of your problem, and that estimate some norm of the error between your computed solution and the exact, unknown one. Since these estimators are local, they help you refine the mesh efficiently by telling you where you should refine it in priority if you want to reduce the error.
In addition, in non-linear problems, they may also tell you when to stop your non-linear iterations (be they of Newton type or fixed-point type for example): it is indeed not useful to solve your non linear system very accurately if the numerical errors due to the mesh are large. The same idea applies to choose a time step that is not unnecessary too small with respect to the mesh size in time-dependent problems.
The derivation of a posteriori error estimators depend on your physical model (the partial differential equations you want to solve) and on the type of discretization (finite elements, finite volumes, DG, ...).
Usefull references are:
A posteriori error estimation in finite element analysis
M Ainsworth, JT Oden
John Wiley & Sons
The finite element method and its reliability
I Babuška, T Strouboulis
Oxford university press
For more advanced and recent research, a good starting point may be the web pages of active researchers in that field:
Martin Vohralik: https://who.rocq.inria.fr/Martin.Vohralik/Pages/PublRevInt.html
Carsten Carstensen: http://www.math.hu-berlin.de/~cc/cc_homepage/bibliography/publications.php
Mark Ainsworth: http://scholar.google.fr/citations?hl=fr&user=Y2xFYY4AAAAJ&view_op=list_works&sortby=pubdate
Hope this helps; best regards,
Pascal Omnes
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