  The discrete unified gas kinetic scheme (DUGKS) is a finite-volume scheme
with discretization of particle velocity space, which combines the advantages
of both lattice Boltzmann equation (LBE) method and unified gas kinetic scheme
(UGKS) method, such as the simplified flux evaluation scheme, flexible mesh
adaption and the asymptotic preserving properties. However, DUGKS is proposed
for near incompressible fluid flows, the existing compressible effect may cause
some serious errors in simulating incompressible problems. To diminish the
compressible effect, in this paper a novel DUGKS model with external force is
developed for incompressible fluid flows by modifying the approximation of
Maxwellian distribution. Meanwhile, due to the pressure boundary scheme, which
is wildly used in many applications, has not been constructed for DUGKS, the
non-equilibrium extrapolation (NEQ) scheme for both velocity and pressure
boundary conditions is introduced. To illustrate the potential of the proposed
model, numerical simulations of steady and unsteady flows are performed. The
results indicate that the proposed model can reduce the compressible effect
efficiently against the original DUGKS model, and the NEQ scheme fits well with
our model as they are both of second-order accuracy. We also implement the
proposed model in simulating the three dimensional problem: cubical lid-driven
flow. The comparisons of numerical solutions and benchmarks are presented in
terms of data and topology. And the motion pattern of the fluid particles in a
specific area is characterized for the steady-state cubical lid-driven flows.
