All that sounds very neat, and from what you're
saying I'm really impatient to see some first tests
and results. For my part, I was just fumbling with
the idea of trying something which crudely models
the behaviour of water, in a much less precise way
than described in all those papers, but which would
be sufficient for a POV-Ray render, taking the long
parsing times into account...
All those difficult equations appear to me like
the system should better be implemented with
C++ or JAVA (JAVA for portability) than
with POV-Script, just because of the speed.


-- 
Tim Nikias v2.0
Homepage: http://www.digitaltwilight.de/no_lights
Email: Tim### [at] gmxde

> For more complex fluid flow simulations, Nick Foster and Ronald Fedkiw's
> SIGGRAPH 2001 paper 'Practical Animation of Liquids'
> (http://www.cis.upenn.edu/~fostern/pdfs/foster_siggraph01.pdf) is
excellent,
> if somewhat advanced for my own maths skills...
>
> You mention that what you're looking for is more like Jos Stam's 'Stable
> Fluids' paper. I've just had a go at modifying his algorithm to apply to
> fluids with a height-field for the air/water boundry, such as the ones
> you're simulating. Instead of treating the fluid as incompressibly as he
> does, I am using a scalar 'height' field as well as a 2d vector velocity
> field to describe the fluid as a 2D compressible one, with the density of
> fluid at each point being represented by the height (i.e. depth) of water
at
> that point.
>
> In my algorithm, first the both height and velocity fields are advected by
> the velocity field as Stam describes in his paper
> (http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/ns.pdf). The
> next stages of the algorithm describe how the height and the velocity of
the
> fluid interact. Firstly, if the velocities of the fluid around a certain
> point are such that more fluid is flowing towards that point than away
from
> it, the height of that point increases to accomodate the extra water.
> Secondly, the velocity field is modified so that at places where there is
a
> 'slope' in the height field, the water tends to run down the slope -
> equivalent to very dense areas of a compressed fluid expanding outwards to
> equalise the pressure.
>
> This algorithm produces some interesting effects, such as realistic wakes
> behind objects. There are still a few bugs to iron out: I suspect that my
> algorithm could be improved, and the advection technique introduces
> significant blurring due to antialiasing if small time steps are used.
> Hopefully I'll get the time to render and post an animation soon to show
> what I mean?
>
> Has anyone else tried a "ground-up" approach to fluid flow in Pov-Ray
(i.e.
> looking at the physics first, then writing the code, rather than basing
the
> code on what looks best)? I'd be most interested to hear from anyone who
> has.
>
>

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