Group: sci.physics.computational.fluid-dynamics
From: mathieu.dutour@gmail.com
Date: Wednesday, November 14, 2007 12:04 PM
Subject: 2D finite volume grid

I am using the finite volume model SUNTANS.
It is an oceanographic model with a vertical stratification, and the
problem is how to
obtain a 2D triangulation from the coastline.

The Temperature, Salinity variable are stored at the vertices of the
triangulation.
The u, v velocity vectors are stored at the center of the Delaunay
circles of
the triangle.

In general I am searching for books, reference explaining finite
volume specifically,
about how such schemes are build. The books I know are kind of evasive
about
the finite volume setting, about the grid generation and the
implementation.

In specific, here is the questions I have:
---What should be the constraints satisfied by the triangulation?
-1- I heard about the angle being at most 90 degrees and in fact 85
deg
being preferable.
-2- One logical constraint would be that the edges should be
relatively long, i.e.
if two Delaunay centers are near then I would believe that
this cause problem
-3- The minimal angle being small. That is a condition that shows
up.
It seems to me that condition 1 is chosen so as to imply condition
2. But I may
be wrong. What would the origin of such conditions? Did I missed
some conditions?
---What methods can be used to generate triangulations.
-1- the method of adding new vertices at centers of empty circles
can ensure
the condition of small angle to be satisfied. This is the
algorithm used by
the program triangle.
-2- there was some work done by Marshall Bern, David Eppstein on
generation
of triangulation with maximal angle by circle packings. But
this does not
seem to be implemented, or possible to implement, in some
existing generation
software.
In a nutshell:
-1- What are the constraints needed by a finite volume 2D grid?
-2- What are the possible algorithms for generating with those
constraints?
-3- What existing software, preferably free, implementing such
algorithms.

Thank you for reading me some far. If you have any help, please send
me info
here or in the group. Really, I lack solid references on which to rely
and I am
open to any suggestions.

Mathieu

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