CODEWITHSUNDEEP
c++simulationfluid-dynamics
qwr
qwr

Reputation: 10919

Fluid simulation incompressible fluid

In the fluid simulation based on a paper by Stam, fluid is modeled as a grid of densities. The densities "usually take a value between zero and one", but can be greater. Boundaries are implemented essentially as described in the paper:

A simple way of implementing internal boundaries is to allocate a Boolean grid which indicates which cells are occupied by an object or not. Then we simply have to add some code to the set_bnd() routine to fill in values for the occupied cells from the values of their direct neighbors. 

int surround = !bound[IX(i+1,j)] + !bound[IX(i-1,j)] + !bound[IX(i,j+1)] + !bound[IX(i,j-1)];
if (!surround) x[IX(i,j)] = 0;
else
    x[IX(i,j)] = ((bound[IX(i+1,j)] ? 0 : x[IX(i+1,j)]) +
                  (bound[IX(i-1,j)] ? 0 : x[IX(i-1,j)]) +
                  (bound[IX(i,j+1)] ? 0 : x[IX(i,j+1)]) +
                  (bound[IX(i,j-1)] ? 0 : x[IX(i,j-1)])) / surround;

The density method works well for compressible fluids like air, fire, or smoke. Is there a method to change boundary routines so density (limited to one fluid) is limited to a value, such as 1? This would represent say a cell completely full of water particles. Density that would be greater than one would have to be pushed away to neighboring cells. Stam lists ideas for extension but does not include how:

Another extension is to use this solver as a basis to animate water flows. In this case there are two fluids with different densities: water and air. The air is usually not modeled and the solver is harder to implement for the following reason: the domain of the water fluid changes over time and has to be tracked somehow and the correct boundary conditions have to be applied at the interface. The water region can be tracked using particles which simply move through the fluid as done by Foster and Metaxas [Foster96] or can be tracked with a combination of particles and level sets [Foster01,Enright02].

Upvotes: 0

Views: 1339

Answers (1)

duffymo
duffymo

Reputation: 308763

I think you should say "incompressible flows with a free surface".

That's a hard problem because you have to track the location of the free surface as a function of space and time.

Densities of all the fluids you name are not equal to one; the paper must normalize them in some way that you don't make clear.

How do you track the free surface? Can a cell have two fluids inside at once, or is it either all water or all air? If it's the latter, that means you've got to have a very fine mesh near the surface to be able to resolve something like a wave propagating in the ocean.

For that problem you can treat both the water and air as incompressible, even though you know that a gas is not. The velocity of the air is low enough where the Mach number is less than 0.1, so compressibility effects are small.

Upvotes: 1

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