A gas-surface interaction algorithm for discrete velocity methods in predicting rarefied and multi-scale flows II: For Cercignani-Lampis boundary model

The discrete velocity method (DVM) for rarefied flows and unified methods based on the DVM framework for flows in all regimes have worked well as precise flow solvers over the past decades and have been successfully extended to other important physical fields. However, these methods primarily focus on modeling gas-gas interactions. For gas-surface interactions (GSI) at the wall boundary, they usually use the full accommodation diffuse reflection model, which cannot accurately describe the behavior of reflected gas molecules in rarefied flows. To overcome this bottleneck and extend the DVM and unified methods to more realistic boundary conditions, a Cercignani-Lampis (CL) boundary with different momentum and thermal energy accommodations is proposed and integrated into the DVM framework. In this work, by giving the macroscopic flux from the numerical quadrature of the incident molecular distribution, the reflected macroscopic flux can be obtained for the given accommodation coefficients. Then, an anisotropic Gaussian distribution can be found for the reflected molecules, whose parameters are determined by the calculated reflected macroscopic flux. These macroscopic flux and microscopic Gaussian distribution form a complete physical process for the reflected molecules. Furthermore, the CL boundary is integrated into the unified gas-kinetic scheme (UGKS), making it suitable for the simulation of both monatomic and diatomic gas flows, and it accommodates both the conventional Cartesian velocity space and the recently developed efficient unstructured velocity space. Moreover, this new GSI boundary is suitable for both explicit and implicit schemes, offering better performance for flow prediction. Finally, the performance of the new boundary is validated through a series of numerical tests covering a wide range of Knudsen and Mach numbers.