1
$\begingroup$

In the Lattice Boltzmann method we require (based on mass conservation) that the sum of the distribution functions for a node is equal to the density, i.e.

$$ \sum_i f_i = \rho $$

But what units do $f_i$ have that make their sum equal to the density, which has units of $kg/m^3$?

I guess it means that $f_i$ must have same units as the density, but how can I interpret $f_i$ in that case?

$\endgroup$
  • 1
    $\begingroup$ By the definition you write down, the unit must be the same as the density $\endgroup$ – unsym Dec 18 '13 at 20:39
2
$\begingroup$

Suppose you want to use real measurements in this equation, then the density is actually the mass $m_0$ contained in a mesh unit volume (or voxel) divided by the volume of the voxel, $a^3$ such that $\rho=m_0/a^3$. As far as I know in the lattice Boltzmann method there is a finite number of velocities $\vec c_i$ and $f_i$ is the mass $m_i$ of matter moving with velocity $\vec c_i$ divided by $a^3$, $f_i=m_i/a^3$. As $\sum_im_i=m_0$, this explains why $\sum_f_i=\rho$. I hope this answers the interpretation part of your question.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.