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

Abstract

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.