  Different molecular dynamics methods like the direct method, the Green-Kubo
(GK) method and homogeneous non-equilibrium molecular dynamics (HNEMD) method
have been widely used to calculate lattice thermal conductivity
($\kappa_\ell$). While the first two methods have been used and compared quite
extensively, there is a lack of comparison of these methods with the HNEMD
method. Focusing on the underlying computational parameters, we present a
detailed comparison of the GK and HNEMD methods for both bulk and vacancy Si
using the Stillinger-Weber potential. For the bulk calculations, we find both
methods to perform well and yield $\kappa_\ell$ within acceptable
uncertainties. In case of the vacancy calculations, HNEMD method has a slight
advantage over the GK method as it becomes computationally cheaper for lower
$\kappa_\ell$ values. This study could promote the application of HNEMD method
in $\kappa_\ell$ calculations involving other lattice defects like nanovoids,
dislocations, interfaces.
