From: a722756@roper.mc.ti.com (W. Donald Rolph)
Subject: Re: Theory about Fluid-Structure ?
Originator: a722756@roper.mc.ti.com
Organization: Texas Instruments / Attleboro Mass / USA
Date: Thu, 21 Jan 1993 18:18:54 GMT


In article <1993Jan21.115722.29874@dutrun2.tudelft.nl>, rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
|> In article <1993Jan20.120623.18611@dutrun2.tudelft.nl>, I wrote:
|> > Wouldn't it help if people first _unify_ F.V. (fluid) and F.E. (solid) 
|> > methods? 
|> 
|> In article <1993Jan20.162622@roper.mc.ti.com> W. Donald Rolph (hi, Don!):
|> > ................... (pardon Han!) the requirement here is that the shape or
|> > trial functiosa [ he means: functions ] across the interface be compatible.
|> > Under these conditions (oh well here we go again) the FV for the fluid
|> > becomes essentially indistinguishable from FEA for the fluid, certainly at
|> > the boundaries at least, and the problem easily reduces to a tractable form.
|> 
|> Oh yeah? Let's take a combustion engine as an example. I have a the solid parts
|> modeled with MARC, and the fluid parts modeled with PHOENICS. According to Don,
|> it would be a "tractable" matter now to roast the beef. 
|> 
|> Or else, let's start from the basics: take some F.E. ingredients for the solid
|> parts, take some F.V ingredients for the fluid parts. Then ... take a BIG MAMA,
|> and "the problem easily reduces to a tractable form".
|> 
|> One world or no world. Once F.V. and F.E. have been unified into ONE universal
|> numerical method, the true practical problems will remain hard enough to solve.
|> -- 
|> * 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

I agree completely with Han.  I pose however, that at least at first pass, the fv
formulation could be established for the fluid matched by trial functions to the
solid with fea and in one single program solve the problem.  Since as posed the
variables would be continuous accross the boundary, the problem is indeed
tractable, as for example Olsen and Bathe Journal of Computer and Structures 21,
1985.

I still pose further, however,  that properly posed the fea equations for the
fluids themselves become indistinguishable form the fv equations for thes fluid
themselves.  Han you have brought up upwind differencing for the convective term
before.  I reference Zienkiewicz 1977 starting on page 633 where he discusses
applying upwind differencing for the convective term using fea procedures.  If
these equations are consistent with your fv upwind differencing, then since you
already conceded that for the pure diffusion problem fea and fv can reduce to the
same form, a common ground would appear to exist.

If the above paragraph sustains critical review, then my position is an even more
optimistic one than yours, that is to say yes we need a merging of the two
techniques - I agree completely, but further that the math to merge the two
techniques already exists.  ONE universal numercal method can be achieved today!

You thoughts Han?

-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263