  Discrete unified gas-kinetic scheme (DUGKS) is a multi-scale numerical method
for flows from continuum limit to free molecular limit, and is especially
suitable for the simulation of multi-scale flows, benefiting from its
multi-scale property. To reduce integration error of the DUGKS and ensure the
conservation property of the collision term in isothermal flow simulations, a
Conserved-DUGKS (C-DUGKS) is proposed. On the other hand, both DUGKS and
C-DUGKS adopt Cartesian-type discrete velocity space, in which Gaussian and
Newton-Cotes numerical quadrature are used for calculating the macroscopic
physical variables in low speed and high speed flows, respectively. While, the
Cartesian-type discrete velocity space leads to huge computational cost and
memory demand. In this paper, the isothermal C-DUGKS is extended to the
non-isothermal case by adopting coupled mass and inertial energy distribution
functions. Moreover, since the unstructured mesh, such as the triangular mesh
in two dimensional case, is more flexible than the structured Cartesian mesh,
it is introduced to the discrete velocity space of C-DUGKS, such that more
discrete velocity points can be arranged in the velocity regions that enclose
large number of molecules, and only a few discrete velocity points need to be
arranged in the velocity regions with small amount of molecules in it. By using
the unstructured discrete velocity space, the computational efficiency of
C-DUGKS is significantly increased. A series of numerical tests in a wide range
of Knudsen numbers, such as the Couette flow, lid-driven cavity flow,
two-dimensional rarefied Riemann problem and the supersonic cylinder flows, are
carried out to examine the validity and efficiency of the present method.
