Fin.Differences and convection-diffusion
F.A.J. Straetemans
Does anyone know a book or a paper in which
the space variables in a convection-diffusion
problem with variable coefficients are discretized
using finite differences with non-equidistant
points?
Many textbooks only deal with constant coefficient
problems and/or equidistant points.
Thanks in advance,
Franc.
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Franc Straetemans , Department of Mathematics & Computer Science
Room 219 , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands
Phone: < 071-5277119 > , Fax: < 071-5276985 >
Email: < fran...@wi.leidenuniv.nl >
WWW: < http://www.wi.leidenuniv.nl/~francstr/ >
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J.Wendelstorf
In article <320756...@wi.leidenuniv.nl> "F.A.J. Straetemans" <fran...@wi.leidenuniv.nl> writes:
>From: "F.A.J. Straetemans" <fran...@wi.leidenuniv.nl>
>Subject: Fin.Differences and convection-diffusion
>Date: Tue, 06 Aug 1996 10:30:11 -0400
>Does anyone know a book or a paper in which
>the space variables in a convection-diffusion
>problem with variable coefficients are discretized
>using finite differences with non-equidistant
>points?
>Many textbooks only deal with constant coefficient
>problems and/or equidistant points.
>Thanks in advance,
>Franc.
I think,
Patankar, Suhas V
"Numerical heat transfer and fluid flow"
Hemisphere Publishing, 1980
is still the standard reference in this area. I used it
for highly nonlinar problems with non-aequidistant grids
and coefficients varying by several orders of magnitude.
Bye, Jens
+----------------+---------------+---------------+----------------------+
|Jens Wendelstorf|Inst.of.Welding+TU-Braunschweig|j.wend...@tu-bs.de|
+----------------+---------------+---------------+----------------------+
F.A.J. Straetemans
J.Wendelstorf wrote:
>
> In article <320756...@wi.leidenuniv.nl> "F.A.J. Straetemans" <fran...@wi.leidenuniv.nl> writes:
> >From: "F.A.J. Straetemans" <fran...@wi.leidenuniv.nl>
> >Subject: Fin.Differences and convection-diffusion
> >the space variables in a convection-diffusion
> >problem with variable coefficients are discretized
> >using finite differences with non-equidistant
> >points?
> >Many textbooks only deal with constant coefficient
> >problems and/or equidistant points.
> Patankar, Suhas V
> "Numerical heat transfer and fluid flow"
> Hemisphere Publishing, 1980
> is still the standard reference in this area. I used it
> for highly nonlinar problems with non-aequidistant grids
> and coefficients varying by several orders of magnitude.
I know this book, I often use it. But it uses finite volume
methods to derive schemes.
The same occurs in a new book I found a few days ago:
Shashkov M. (1996): Conservative finite-difference methods on general
grids, CRC Press (New York).
In this book finite difference schemes are derived using finite
volume ideas. Of course the resulting scheme can be formulated
as a finite difference scheme, but I wondered if people obtained schemes
in another way, by just replacing the space derivatives by difference
formulas.
Franc
Elias Kougianos
>
>I know this book, I often use it. But it uses finite volume
>methods to derive schemes.
>The same occurs in a new book I found a few days ago:
> Shashkov M. (1996): Conservative finite-difference methods on general
> grids, CRC Press (New York).
>In this book finite difference schemes are derived using finite
>volume ideas. Of course the resulting scheme can be formulated
>as a finite difference scheme, but I wondered if people obtained schemes
>in another way, by just replacing the space derivatives by difference
>formulas.
>
>Franc
>
>******************************************************************
>
> Franc Straetemans , Department of Mathematics & Computer Science
> Room 219 , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands
> Phone: < 071-5277119 > , Fax: < 071-5276985 >
> Email: < fran...@wi.leidenuniv.nl >
> WWW: < http://www.wi.leidenuniv.nl/~francstr/ >
>
>******************************************************************
Take a look at:
Ballester & Pereyra, "On the Construction of Discrete Approximations
to Linear Differential Expressions", Math. Comp., vol. 21, pp.
297-302, 1967
on how to setup the dicretization equations for a 1-D problem and look
at:
Bj\o"rck & Pereyra, "Solution of Vandermonde Systems of Equations",
Math. Comp., vol. 24, No. 112, pp.893-903, 1970
on how to solve them efficiently.
Then look at
Galimberti & Pereyra, "Numerical Differentiation and the Solution of
Multidimensional Vandermonde Systems", Math. Comp., vol. 24, No. 110,
1970
for the generalization in more than 1 dimension.
Good luck.
==============================================================
Elias Kougianos
el...@premier.net