  In this paper, we proposed a central moment discrete unified gas-kinetic
scheme (DUGKS) for multiphase flows with large density ratio and high Reynolds
number. Two sets of kinetic equations with central-moment-based multiple
relaxation time collision operator are employed to approximate the
incompressible Navier-Stokes equations and a conservative phase field equation
for interface-capturing. In the framework of DUGKS, the first moment of the
distribution function for the hydrodynamic equations is defined as velocity
instead of momentum. Meanwhile, the zeroth moments of the distribution function
and external force are also suitably defined such that a artificial pressure
evolution equation can be recovered. Moreover, the Strang splitting technique
for time integration is employed to avoid the calculation of spatial
derivatives in the force term at cell faces. For the interface-capturing
equation, two equivalent DUGKS methods that deal with the diffusion term
differently using a source term as well as a modified equilibrium distribution
function are presented. Several benchmark tests that cover a wide a range of
density ratios (up to 1000) and Reynolds numbers (up to $10^5$) are
subsequently carried out to demonstrate the capabilities of the proposed
scheme. Numerical results are in good agreement with the reference and
experimental data.
