Comment by gus_massa | Hacker News Reader

Comment by gus_massa | Hacker News Reader

> Of course, this model isn't perfect. One of the most obvious problems is that it doesn't have inertia and velocity diffusion. A fast water stream entering a lake won't propagate further inside the lake, but will instead spread out in all directions, ignoring all accumulated inertia. Two parallel water streams going in opposite directions can exist and not interact with each other (provided the water levels are equal).

I guess that can be solved averaging he value of a flow arrow with the 6 neighbor arrows in the same direction. With a big weight with the arrows that are in the front and back, and a small weight for the arrows that are on the sides. For example with these arrows

     -a->  -b->

  -c-> -d->  -e->

     -f->  -g->

then

  New_d = d * (1 - 2*.1 - 4*.01) + (c+e)*.1 + (a+b+f+b)*.01

Where .1 and .01 are weight that I just invented but must be tweaked, perhaps with a power like the one they use to kill osculations. That coefficient can also be included:

  New_d = d * (1 - 2*.1 - 4*.01 - .001) + (c+e)*.1 + (a+b+f+b)*.01

I would say the proper solution is to add another grid for the second derivative, this time matching the original grid. That is

grid 0: water height in each cell

grid 1: water flow at each edge (first derivative)

grid 2: water acceleration in each cell (second derivative)

So each grid is the dual of the previous one and stores its derivative. In fact I don't think you even need to store edge data as a special case, just corner data and work purely with dual grids. You can derive the edge flow by taking the sum of the flow at the two corners of the edge. So you update the fluid height based on flow, then you update acceleration based on how much fluid mass flowed into the cell with what velocity, then you update the flow based on acceleration and current fluid height. I don't really know fluid dynamics, but looking at it purely from a numerical simulation standpoint, it sounds about right. It would also let you have diagonal flow.

That violates conservation of momentum. To get realistic flow, you need to use continuity equation to preserve the energy of the flow and let the shear dissipate and diffuse into whorls. Which is a lot of extra calculation, as pointed out in the article, so you need to ask yourself if that level of realism is really necessary for your use case.

The first evacuation (without the dumping coefficient)

  New_d = d * (1 - 2*.1 - 4*.01) + (c+e)*.1 + (a+b+f+b)*.01

is as good as conserving momentum as the original model. (Assuming you calculate all the new values using a new matrix instead of overwriting the old ones.) It breaks energy conservation, but that simulates the friction between oposite direction currents, without going to the whorls level.

I agree that this is not 100% realistic, but I think it's a good and simple addition to the model in the article, and tweaking the coefficients it may give a good enough visual result.

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