FEM v's FVM
Hi everybody,
I have a problem that I am trying to find a straight forward answer on i.e. reams of theoretical derivations does not do it for me... I ran a certain grid independant mesh using FEM and FVM and I plotted the results for the wall shear rates. Though the models had the exact same flow conditions and the model was grid independant the results were quite different. They are two different solvers and there must be expected to be different results due to discretisation, however I need to know what the reason between the way they calculate wall shear rates. Is it due to the interpolation methods used to the cell nodes? Has anybody else done FEM/FVM comparisons? Thanks for any comments, Tommy. 
Re: FEM v's FVM
1) In theory, if convergence towards the true solution can be proved for both of your scheme, there shouldn't be any significant difference between your results;
2) There might be stability constraints that have not been met for one of your schemes; 3) Look for any errors in the implemetation of the BC's if these problems involved more complex situations. 4) Before solving any "real life problem" try to validate your schemes with many benchmark solutions. Good Luck. 
Re: FEM v's FVM
Hi,
Most important concept in CFD is "consistency and stabilty" which needs to be satisfied while developing a numerical algorithm. How can you have two different solutions for the same problem? You could have gone wrong in implimenting the boundary conditions through which "physics" enters the problem. First check your algorithm/numerical scheme,then check your code for possible bugs and then take a benchmark solution which will certainly tell you where the problem is(atleast you will know whether there is a bug in your code or not). I haven't done any FEM computations but only FVM. regards gita 
Re: FEM v's FVM
Thanks for your responses. The interesting thing about my comparisons is that both the FEM and FVM models have been experimentally validated using velocity profiles and give good agreement. However in comparing the wall shear stresses which cannot be determined experimentally there is a significant difference. I have tried to be consistent in setting up both of the models, i.e. grid independence, convergence, solution method, however, the differences remain. I think that it is possible that the difference lies in the way the solver calculates the shear rate at the wall. I am unsure as to the differences between the two methods I am using, and the manuals are not particularly clear. Neither of the methods are more/less accurate, they are different methods and conclusions must be drawn accounting for this. Thank you, Tommy.

Re: FEM v's FVM
Hi Tommy,
What is the magnitude of the difference? Are your results qualitatively the same(wall shear stress)? Maybe someone with better expertise along these lines able to answer you. Are you using your own code or some commercial software? Is your study on the comparison of FEM vs FVM? BTW, why do you want to test both? gita 
Re: FEM v's FVM
Hey Gita,
My results are qualitatively the same, Its just that for wall shear stress FVM (Fluent) is consistently higher than FEM (FIDAP). The comparison is being made between FEM and FVM. I am testing both because they are totally different efficiency wise, userfriendliness, and even it seems accuracy. It seems that the answer lies in the FEM use of shape functions at the wall unlike FVM which uses value stored at cell centre. I wish there was a book in english that explained all the concepts that these solvers are built on. Thanks, Tommy. 
Re: FEM v's FVM
Hi Tommy,
Your problem seems interesting to me. So what is the difference(quantitative) in wall shear stress using the two different approaches? I have done some homeworks using FEM and that's it. I always wonder why there are few who use FEM in fluids. I haven't come across any book which pins down the distinction between the two methods. Do you have to live with this deviation in the two methods?? If shape fn determines the correct solution,how do you choose them correctly apriori? You can send mails to my email id. gita 
Re: FEM v's FVM
Hi guys,
This was post by Herve on 17 January on the main forum. "Look at the book edited by 33. Wendt, J.F., (1996), "Computational Fluid Dynamics An Introduction", Springer. or the paper by Idelsohn, S.R., Oņate, E., (1994), "Finite Volumes and Finite Elements: Two 'Good Friends'", Int. J. num. Meth. Eng., Vol. 37, pp. 33233341. for a comparison. the advantage of FVM is that it is easy and fast to compute, and mass conservative (something more difficult to achieve with FEM I believe)". I haven't seen this paper but i though it might be of use to you. 
Re: FEM v's FVM
Thanks guys for all your thoughts. Tommy.

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