Computing divergence of gradient in a field with measured velocity vectors

I am currently trying to implement a particle simulation with the Lattice Boltzmann Method. The current task is to use the following equation to calculate the kinematic viscosity of the medium:

$frac{partial u}{partial t} = nu * Delta u$

Where $u$ is a two dimensional field of two dimensional velocity vectors and $nu$ is the unknown viscosity. By running a couple of simulation steps, it is possible to measure the change of velocity over time $frac{partial u}{partial t}$. But how would you calculate the $Delta u$ from the measured values $u$? Wikipedia reads:

$Delta f = sum_{i=1}^{n} frac{partial² f}{partial x_i²}$

Unfortunatly I am having a hard time finding examples online, since a lot of examples assume, that $f(x_1,x_2)$ is function directly computable from $x_1$ and $x_2$.