If the collision does not occur at the point of the network, but at a distance \Delta:

\\n\\nthen the function must consider the offset by weighting the contributions\\n\\n

$f_i(x_f,t+\delta t)=\displaystyle\frac{(1-\Delta)f_{-i}(x_f,t)+\Delta(f_{-i}(x_b,t)+f_{-i}(x_{f2},t)}{1+\Delta}$

(ID 8499)

If the wall shows an inclination with respect to the network it must be modeled in a more complex form:

More general edge

First, an approximate boundary must be defined to allow the necessary edge equations to be established. Then they must be applied in the process of steraming.

(ID 8500)

In the streaming process the particles are moved according to their velocity directions to neighboring cells

where \vec{x} is the position, t time, \vec{e} _i the direction of the grid and c the speed.

(ID 9150)

In the case of a D2Q9 system we have the 9 values f_i that we have named as O, N, E, S, W, NE, SE, SW, NW. If the number of particles in position (n,m) is denoted as f_i(j,k) we have that the equations are

```

N[x,y] = N[x,y-1]

NW[x,y] = NW[x+1,y-1]

E[x,y] = E[x-1,y]

NE[x,y] = NE[x-1,y-1]

S[x,y] = S[x,y+1]

SE[x,y] = SE[x-1,y+1]

W[x,y] = W[x+1,y]

SW[x,y] = SW[x+1,y+1]

```

(ID 9151)