Cryogenic carbon capture (CCC) can preferentially desublimate
$\text {CO}_2$
out of the flue gas. A widespread application of CCC requires a comprehensive understanding of
$\text {CO}_2$
desublimation properties. This is, however, highly challenging due to the multiphysics behind it. This study proposes a lattice Boltzmann (LB) model to study
$\text {CO}_2$
desublimation on a cooled cylinder surface during CCC. In two-dimensional (2-D) simulations, various
$\text {CO}_2$
desublimation and capture behaviours are produced in response to different operation conditions, namely, gas velocity (Péclet number
$\textit {Pe}$
) and cylinder temperature (subcooling degree
$\Delta T_{sub}$
). As
$\textit {Pe}$
increases or
$\Delta T_{sub}$
decreases, the desublimation rate gradually becomes insufficient compared with the
$\text {CO}_2$
supply via convection/diffusion. Correspondingly, the desublimated solid
$\text {CO}_2$
layer (SCL) transforms from a loose (i.e. cluster-like, dendritic or incomplete) structure to a dense one. Four desublimation regimes are thus classified as diffusion-controlled, joint-controlled, convection-controlled and desublimation-controlled regimes. The joint-controlled regime shows quantitatively a desirable
$\text {CO}_2$
capture performance: fast desublimation rate, high capture capacity, and full cylinder utilization. Regime distributions are summarized on a
$\textit {Pe}$
–
$\Delta T_{sub}$
space to determine operation parameters for the joint-controlled regime. Moreover, three-dimensional simulations demonstrate four similar desublimation regimes, verifying the reliability of 2-D results. Under regimes with loose SCLs, however, the desublimation process shows an improved
$\text {CO}_2$
capture performance in three dimensions. This is attributed to the enhanced availability of gas–solid interface and flow paths. This work develops a reliable LB model to study
$\text {CO}_2$
desublimation, which can facilitate applications of CCC for mitigating climate change.