  The discrete velocity method (DVM) for rarefied flows and the unified methods
(based on the DVM framework) for flows in all regimes have proven to be
effective flow solvers over the past decades and have been successfully
extended to other important physical fields. Both DVM and unified methods
strive to physically model gas-gas interactions. However, for gas-surface
interactions (GSI) at the wall boundary, they have only used the full
accommodation boundary until now, which deviates from reality. Moreover, the
accommodation degrees of momentum and thermal energy are often different. To
overcome this limitation and extend the DVM and unified methods to more
realistic boundary conditions, an algorithm for the Cercignani-Lampis (CL)
boundary with different accommodation degrees of momentum and thermal energy is
proposed and integrated into the DVM framework. A Gaussian distribution with
slip velocity, including several undetermined parameters, is designed to
describe the reflected distribution function. Once the accommodation
coefficients (ACs) are known, these undetermined parameters are solved using
the relationship between ACs and reflected macroscopic fluxes. In this paper,
the Maxwell model and CLL model are adopted as benchmarks to evaluate the
performance of the proposed CL model. Additionally, the current CL boundary for
the DVM framework considers generality, accommodating both the recently
developed efficient unstructured velocity space and the traditional Cartesian
velocity space. Moreover, the proposed CL model allows for calculations of both
monatomic gases and diatomic gases with internal degrees of freedom. Finally,
by being integrated with the unified gas-kinetic scheme within the DVM
framework, the performance of the present CL model is validated through a
series of benchmark numerical tests across a wide range of Knudsen numbers.
