Thread View: sci.math.num-analysis
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Started by Han de Bruijn
Mon, 14 Dec 1992 13:24
RE: Comparison between FEM and FDM/CVM for fluid flow modeling
Author: Han de Bruijn
Date: Mon, 14 Dec 1992 13:24
Date: Mon, 14 Dec 1992 13:24
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In article <1992Dec11.165920.3016@magnus.acs.ohio-state.edu> Shekhar Damle: > Besides the ability to model complex geometries, what are the advantages > of FEM over the more established Finite Difference Methods(FDM) or Control > Volume Methods (CVM) when it comes to fluid flow modeling ? None. > Does the situation change if fluid flow is coupled with heat transfer as > has to be done while modeling solidification ? No. > Is the situation different if the flow is turbulent ? No. > The reason I raise these questions is that I do not know of any other > advantages of FEM vis-a-vis fluid flow modeling. I do not consider myself > to be an expert in CFD by any means and I am quite willing to change my mind. > (Of course it goes without saying that the ability to model complex geometries > can be quite significant in many situations) So far so good. Are we truly willing to change our mind? How about the idea to CHANGE both nowadays FDM and FEM methods? In fact, nowadays FVM and FEM represent totally different _cultures_, and it's very difficult, sometimes even dangerous, to cross over from one champ to the other. But perhaps _that_ should represent a challenge for everybody who is working in the field. Or are we too "pragmatic", too busy with our "demanding applications" to consider such a thing? SUNA = Series on Unified Numerical Approximations. Numerical methods are not a gift from the gods. They were invented by humans, and the same humans are free to change the boundary conditions. SUNA articles are available now on a (more or less) permanent basis, via "anonymous ftp". They can be retrieved as follows: ftp dutrde1.tudelft.nl (: internet-adress = 130.161.180.13) Name: (: "anonymous") Password: (: <user>@<host> ) cd pub/suna ls (: list of "suna*.net" articles) mget <filenames> See also "SUNA, Published so far" for the complete list of available articles; it is contained in the file: "sunall.net". Not everything may be of interest. Articles may be outdated and sometimes even wrong. Start with "The Manifesto". Gee, it's indeed high time to clean up this stuff ... - * Han de Bruijn; Applications&Graphics | "A little bit of Physics * No * TUD Computing Centre; P.O. Box 354 | would be NO idleness in * Oil * 2600 AJ Delft; The Netherlands. | Mathematics" (HdB). * for * E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood
Re: Comparison between FEM and FDM/CVM for fluid flow modeling
Author: Fred Walsteijn
Date: Mon, 14 Dec 1992 23:16
Date: Mon, 14 Dec 1992 23:16
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In <1992Dec14.132457.24381@dutrun2.tudelft.nl> rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes: >In article <1992Dec11.165920.3016@magnus.acs.ohio-state.edu> Shekhar Damle: >> Besides the ability to model complex geometries, what are the advantages >> of FEM over the more established Finite Difference Methods(FDM) or Control >> Volume Methods (CVM) when it comes to fluid flow modeling ? >None. >> Does the situation change if fluid flow is coupled with heat transfer as >> has to be done while modeling solidification ? >No. >> Is the situation different if the flow is turbulent ? >No. I disagree. Galerkin methods have the advantage that without much effort (for example quadratic) conservation properties hold in the (semi-) discrete system too. This is known to be important if ``viscosity is low''. For example in 2-D turbulence usage of linear FEM methods leads to conservation of (semi-) discrete energy and enstrophy. That's true even for complicated domains. (Arakawa's special FD discretization is identical to such a method in cartesian domains/grids but required a much more complicated derivation.) It turns out that even in poorly resolved flows (as is usual in turbulence simulations) the discrete energy cascade behaves much like the real thing. A non-conserving method would produce inferior results (inaccuracies and possibly instabilities) much earlier in the process of increasing Reynolds number. Nice examples can also be found in the book of Canuta et al (Spectral methods, Springer Verlag ?) for MHD simulations. Note that conservation is not a complete guarantee for accuracy: if the viscosity is very low (resolution much too coarse) then discrete artefacts will show up. In 2-D turbulence: so-called enstrophy equipartitioning. The remaining advantage is that in these cases the Galerkin method is nonlinearly stable, while simple centered FD & FV schemes would have exploded ``yesterday''. :-) Hmm. I hope this helps a bit... Good luck, Fred. ----------------------------------------------------------------------------- Fred Walsteijn | Internet: walsteyn@fys.ruu.nl Institute for Marine and Atmospheric Research | FAX: 31-30-543163 Utrecht University, The Netherlands | Phone: 31-30-533169
Re: Comparison between FEM and FDM/CVM for fluid flow modeling
Author: W. Donald Rolph
Date: Tue, 15 Dec 1992 14:22
Date: Tue, 15 Dec 1992 14:22
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There is, however, no requirement that either FVM or FEA to either be conservative or nonconservative (Oden has some nice mathematics describing requirments for conservation in FEA fluid mechanics). The issue remains the shape or approximation functions. Chooses identical shape funcitons and FVM and FEA are identical. Choose bad ones, and both fail. Fundamentally all numerical procedures for PDE approximation have a basic underlying comonality: minimizing error in the approxiamtion funcitons with respect to the actual solution. We realy need to get away from these parochial battles over differences in what are in fact identical procedures. -- Regards. Don Rolph a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263
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