🚀 go-pugleaf

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