Whether "Grid Independent Test" and "Mesh Convergence Study" are synonymous or any difference exists between them? Can anybody explain?
A mesh convergence test should mean computing the solution on successively finer grids. The difference between two refinements is usually taken as a measure of the accuracy of the coarser of the two. (Note that unless you have proven that your scheme will converge there is no guarantee that either of the two is close to the solution.) It will never show an independence unless the difference is of the order of machine zero. On the contrary, if two refinements hardly differ it means that there is no convergence and something is likely to be seriously wrong. Grid independent test appears to mean the same thing but the name is non-sensical since no, or at least very,very few, numerical entities are ever grid independent.
It is synonymous. Both refer to the independency of grid or mesh on the accuracy of the solution. By mesh convergence test (or grid independent test) the computational cost is reduced without compromising with accuracy of the solution.
A mesh convergence test should mean computing the solution on successively finer grids. The difference between two refinements is usually taken as a measure of the accuracy of the coarser of the two. (Note that unless you have proven that your scheme will converge there is no guarantee that either of the two is close to the solution.) It will never show an independence unless the difference is of the order of machine zero. On the contrary, if two refinements hardly differ it means that there is no convergence and something is likely to be seriously wrong. Grid independent test appears to mean the same thing but the name is non-sensical since no, or at least very,very few, numerical entities are ever grid independent.
Both are the same meaning although some says grid independent test & some mesh convergence study and this is a way to find an optimum grid size for a particular simulated problem after this size the solution wont be effected by irrespective of increasing grid size.
An optimal grid can only be defined in relation to an error tolerance. One could say that x per cent difference in the L2 norm of the error is an acceptable accuracy and call that grid size optimal. (Keeping in mind that this is not really the true error.) However, if the numerical scheme is consistent and stable it is only when machine zero is dominating the error that "grid indepence" can be claimed to have been reached.
The CFD solution is never trusted unless the solution is grid converged to an acceptance level of tolerance and/or compared with accurate experimental data.
Usually we do start the CFD solution with coarser grids to save time and get a quick, however might not be accurate results. One, however, expects that as the number of grid points/meshes is increased, the error in the numerical solution would decrease and the agreement between the numerical and exact solutions would be better. When the numerical solutions obtained on different grid/mesh levels agree within a level of tolerance specified by you, the solution is referred to as “grid converged”. This concept of grid convergence applies to the FDM as well as to FVM.
In agreement with other colleagues, I would say that "grid Independent test" and "Mesh Convergence Study" are the same.
@ Zanoun - Thanks for your very informative response - "This concept of grid convergence applies to the FDM as well as to FVM." - Why grid convergence is not applicable in FEM?
From my understanding, I think it is the same meaning because, it is not logical to test or do grid independent test without ensuring this mesh is convergence, In other words, when the solution stop changing or the change is slightly small compared with previous value.so Grid Independent Test" and "Mesh Convergence Study are similar.
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