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The rarefied flow and multi-scale flow are crucial for the aerodynamic design of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete velocity space, the discrete velocity method (DVM) and unified methods can capture complex and non-equilibrium distribution functions and describe flow behaviors exactly. The unified methods predict flows from continuum to rarefied regimes by adopting unified modeling, and they can be further applied to other multi-scale physics such as radiation heat transfer, phonon heat transfer and plasma. In the flow field, the concrete dynamic process needs to describe the gas-gas interaction and gas-surface interaction (GSI). However, in both DVM and unified methods, only a simple but not accurate GSI is used, which can be regarded as a Maxwell GSI with a fixed accommodation coefficient of 1 (full accommodation) at the present stage. To overcome the bottleneck in extending DVM and unified methods to the numerical experiment and investigate real multi-scale flow physics, this paper realizes precise GSI in the DVM framework by constructing the boundary conditions of a concrete Maxwell GSI with an adjustable accommodation coefficient. In the constructing process, the problems of macro-conservation and micro-consistency in the DVS at the boundary are well solved by reflected macroscopic flux and interpolation distribution function and interpolation error correction, respectively. Meanwhile, considering that the multi-scale flows in the background of aeronautics and aerospace are often at supersonic and hypersonic speeds, the unstructured velocity space (UVS) is essential. From the perspective of generality, the GSI is forced on UVS. Besides, by combined with the unified method (the unified gas-kinetic scheme in the paper), the effectiveness and validity of the present GSI on the DVM framework are verified by a series of simulations.