The study of coherent Rayleigh-Brillouin scattering in multiple flow regimes using unified gas-kinetic scheme
Xiaozhe Xi, Junzhe Cao, Kun Xu
TL;DR
The paper develops a unified, multiscale CFD approach to coherent Rayleigh–Brillouin scattering (CRBS) by extending the Unified Gas-Kinetic Scheme (UGKS) to CRBS with a BGK-Shakhov collision model and a Strang splitting strategy to handle the optical dipole force source. The method couples free transport and collisions intrinsically, enabling accurate CRBS simulations across a wide range of Knudsen numbers without stringent resolution requirements. Validation against argon experiments and comparison with Pan’s S6 model establish the accuracy of the approach, and systematic studies reveal how Knudsen number and laser-intensity perturbations shape CRBS spectra, including transitions from Brillouin-dominated to Rayleigh-dominated regimes. The results broaden the applicability of CFD-based CRBS simulations, providing a robust foundation for high-intensity, multiscale gas-kinetic investigations and future extensions to polyatomic gases.
Abstract
Coherent Rayleigh-Brillouin scattering (CRBS) holds great promise for the characterization of gas properties and the investigation of gas kinetic processes. The CRBS spectrum exhibits a strong dependence on the Knudsen number (Kn), revealing its inherently multiscale nature. In the unified gas-kinetic scheme (UGKS), collisions are intrinsically coupled with free transport during flux construction, endowing the method with distinct multiscale capabilities. Specifically, the UGKS reduces to a Boltzmann solver when the relaxation time is greater than or equal to the time step, and to the gas-kinetic scheme (GKS)-a Navier-Stokes solver-when the relaxation time is much smaller than the time step, thereby accommodating flow regimes without constraints on the molecular mean free path or collision time. In this study, the UGKS is extended to simulate CRBS phenomena, with the governing equation formulated based on the BGK-Shakhov model. Detailed derivations are provided. To account for the additional perturbation source term, a second-order accurate numerical algorithm is developed using the Strang splitting method within the UGKS framework. The proposed model is validated against argon CRBS experiments, demonstrating excellent agreement. Building on this validated framework, the impact of incident signal intensity on CRBS spectra across a range of Knudsen numbers is systematically examined, accompanied by an in-depth analysis of the underlying physical mechanisms. This work broadens the applicability of CFD-based CRBS simulations and provides a reliable numerical foundation for exploring high-intensity, multiscale gas-kinetic phenomena in future research.