So this is a little bit in too involved, but let me describe the way.

The first one is hydraulics simulation for a global network.

Here, input is node inflow Qn, so how much flow comes in from the node.

And then what we compute is pipe flow from node inflow.

And hydraulics is a simplified computational method directly computed

from compute from node inflow, and to get a pipe flow.

And after pipe flow, we can compute a pressure, pressure drop at each pipe.

And then from pipe pressure drop, we can

compute the node pressure inside of each node.

And you can get these all information by solving a linear global system once.

It's very fast and it's very efficient.

And after computing pressure node, and pre- pipe flow, we

now switch to the regional details. So for each local region.

We compute, we divide into a lots of grid cells

like this one, and for each grid cell, we compute pressure

and velocity, and in order to compute individual pressure and velocity, we

use a very standard established fluid equation called Navier-Stokes Equation.

So this one is a little bit complicated, but

essentially this just explains the relationship with fluid velocity

and fluid pressure, you know, if there's a huge

difference in fluid pressure, and it causes velocity, and so.

And this step basically just solved this equation times

step, each time step on this grid cells inside each region, to get an animation.