# What is “u” and “v” in this Navier Stokes implementation?

while ( simulating )
{
get_from_UI ( dens_prev, u_prev, v_prev );
vel_step ( N, u, v, u_prev, v_prev, visc, dt );
dens_step ( N, dens, dens_prev, u, v, diff, dt );
draw_dens ( N, dens );
}


Is u,v the same as x,y?

So, yes and no. According to your paper, u and v are vector fields.

As read on the bottom of Page 3:

In practice we allocate two arrays for both the density and the velocity of size,

size=(N+2)*(N+2):static u[size], v[size], u_prev[size], v_prev[size];static dens[size], dens_prev[size];

U and V contain an array of vectors for each 'grid'- this method takes the particles that end up at grid 'centres' and backtraces them compared to a previous snapshot. In other words:

1) Take a snapshot;

2) Run for a bit of time;

3) Take an end snapshot and look at the points that ended up in grid centres;

4) Look at where these points were at the start;

5) Draw a nice smooth line between the start and end points

6) Call it a vector.

In this paper, u is the field of x coordinates for the vectors and v is the field of vector y coordinates. I appreciate it's a longwinded post, but I feel I'd be being cruel just to say 'yeah sure' because it's not actually the answer.

Of course, I'm sure you'll be able to work out that u_prev and v_prev are just the coordinates before the timer started.

Hope it helps!

• Wow! Thank you so much! I am so impressed you were able to look at it and decipher the information, especially for a little ol' stack overflow post! Have a wonderful day. – Dinosaurs for Friends Sep 16 '19 at 22:56