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- Newsgroups: sci.math.num-analysis
- Path: sparky!uunet!mcsun!sun4nl!ruuinf!ruunfs.fys.ruu.nl!walsteyn
- From: walsteyn@fys.ruu.nl (Fred Walsteijn)
- Subject: Re: Comparison between FEM and FDM/CVM for fluid flow modeling
- Message-ID: <1992Dec14.231625.11012@fys.ruu.nl>
- Organization: Physics Department, University of Utrecht, The Netherlands
- References: <1992Dec14.132457.24381@dutrun2.tudelft.nl>
- Date: Mon, 14 Dec 1992 23:16:25 GMT
- Lines: 43
-
- 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
-