$f$	probability density
$M$	3-dimensional array
$\rho$	a small positive value
$n_{neighbor}$	a small positive integer
$v$	volume of the cube
$u$	probability density
$v_g$	total volume of the particles
$\alpha$	volume fraction
$n$	particle number
$M_k$	number of repeated generation position
$c_1$	a positive constant
$ϵ$	number of all random numbers
$g$	discrete distribution function
$e$	velocity space
${\delta }_t$	discrete time step
$t$	current time step
$\Omega$	change caused by collision
$C_s$	lattice velocity
$\omega$	weight coefficient
$\widehat{\sigma }$	fluid velocity
$\sigma$	Darcy velocity
$h$	permeability of porous media
$p_l$	fluid pressure
$\nabla$	Hamiltonian operator
$\widehat{\kappa }$	predicted value of permeability
$\lambda$	rate parameter of the exponential distribution