a	thermal diffusivity
D3Q15, D3Q19	LBM schemes
{ei}	set of discrete speeds
Fi	external forces
$f_k\left(x,y,z,t\right)$	particle distribution function
$f_k^{eq}\left(x,y,z,t\right)$	equilibrium distribution function
IN	nucleation condition
IG	grain growth condition
It	transition condition
IB	condition “at the grain boundary”
kv	velocity coefficient
kq	specific enthalpy coefficient
nx, ny, nz	number of nodes
q 0	initial state
q 1	frontal state
q 2	cell at the grain boundary
q 3	cell in the middle of the grain
q 4	transition state
Q	heat source
Q = {q0, q1, q2, q3, q4}	set of frontal cellular automata states
Q(x,y,z,t)	the source of thermal energy
S	source term
tsteps	number of time steps
Δt	time step
T	temperature
TI	interface temperature
TP	temperature of phase transformation
Tx,y,z	node temperature
v	boundary velocity
wk	weighting factor in direction k
x, y, z	position of the node
Δx, Δy, Δz	grid step
Σ	alphabet
δ	transition rules
ρ	density
ρv	moment
τ	relaxation time
τT	relaxation time for heat transfer (diffusion)
ΔϕI	quantity, mass, or volume of the transformed material in interface node
ϕIα	fractions of ferrite (α) in interface node
ϕIγ	fractions of austenite (γ) in interface node
ω	collision frequency