  With a noticeable increase in research centered on modeling micro fluid
interfaces in the framework of mesoscopic methods, we conduct an exhaustive
study of discrete unified gas-kinetics scheme (DUGKS) in handling complicated
interface deformations. High-order isotropic finite-difference schemes are
first utilized in DUGKS to improve its capability in tracking interfaces. The
performance of third-stage third-order DUGKS where source term is incorporated
has also been assessed for the first time and a series of numerical tests have
been conducted to investigate their capability. The comparative analysis have
revealed the reason why the performance of lattice Boltzmann method is superior
to that of discrete velocity method and DUGKS in general condition from an
informed perspective. The mechanism behind the performance distinction between
the central scheme and upwind scheme utilized in meso-flux construction in
DUGKS have also been clarified. Numerical results have shown that the
employment of high-order schemes in DUGKS does have an effect on the reduction
of numerical dissipation, but the overall accuracy of this method is limited by
the precision of prediction of source terms on mesh interface. The capability
of third-stage third-order DUGKS is severely inhibited by its intrinsic
limitation of the ratio of time step to particle collision time. Among the
various kinds of DUGKS employed with different reconstruction methods, the most
promising scheme is the one with third-order isotropic reconstruction and
upwind-based meso-flux evaluation, which is able to ensure an unique balance
between efficiency and accuracy.
