  The main objective of this work is to perform a detailed comparison of the
lattice Boltzmann equation (LBE) and the recently developed discrete unified
gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the
decaying homogeneous isotropic turbulence (DHIT) in a periodic box. The flow
fields and key statistical quantities computed by both methods are compared
with those from pseudo-spectral (PS) method. The results show that the LBE and
DUGKS have almost the same accuracy when the flow field is well-resolved, and
that the LBE is less dissipative and is slightly more efficient than the DUGKS,
but the latter has a superior numerical stability, particularly for high
Reynolds number flows. Therefore, the DUGKS method can be viewed as a viable
tool for DNS of turbulent flows. It should be emphasized that the main
advantage of the DUGKS when compared with the LBE method is its feasibility in
adopting nonuniform meshes, which is critical for wall-bounded turbulent flows.
The present work provides a basis for further applications of DUGKS in studying
the physics of the turbulent flows.
