  The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV)
scheme for continuum and rarefied flows which combines the benefits of both
Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By
reconstruction of gas distribution function using particle velocity
characteristic line, flux contains more detailed information of fluid flow and
more concrete physical nature. In this work, a simplified DUGKS is proposed
with reconstruction stage on a whole time step instead of half time step in
original DUGKS. Using temporal/spatial integral Boltzmann Bhatnagar-Gross-Krook
(BGK) equation, the transformed distribution function with inclusion of
collision effect is constructed. The macro and mesoscopic fluxes of the cell on
next time step is predicted by reconstruction of transformed distribution
function at interfaces along particle velocity characteristic lines. According
to the conservation law, the macroscopic variables of the cell on next time
step can be updated through its macroscopic flux. Equilibrium distribution
function on next time step can also be updated. Gas distribution function is
updated by FV scheme through its predicted mesoscopic flux in a time step.
Compared with the original DUGKS, the computational process of the proposed
method is more concise because of the omission of half time step flux
calculation. Numerical time step is only limited by the Courant-Friedrichs-Lewy
(CFL) condition and relatively good stability has been preserved. Several test
cases, including the Couette flow, lid-driven cavity flow, laminar flows over a
flat plate, a circular cylinder, and an airfoil, as well as micro cavity flow
cases are conducted to validate present scheme. The numerical simulation
results agree well with the references' results.
