A novel linear stability method based on Shakhov Bhatnagar–Gross–Krook equations for Rayleigh–Bénard convection in rarefied gases

In light of the limitations of the traditional Navier–Stokes (NS) equations in rarefied gas flows, this paper proposes a flow stability analysis method based on Shakhov Bhatnagar–Gross–Krook (S-BGK) equations to investigate the instability of Rayleigh–Bénard convection in rarefied gases. The study explores the effects of the Knudsen number (Kn), the Froude number (Fr), the temperature ratio, and the Prandtl number (Pr) on flow stability. The results indicate that as Kn increases, the linear stability equations (LSEs) based on Navier–Stokes equations (NS-LSEs) tend to underestimate the growth rate. Analysis of the effects of Kn and Fr reveals that the most unstable mode transitions with changes in these parameters. In addition, the effects of temperature ratio and Pr on the stability present different trends: an increase in the temperature ratio stabilizes the flow, whereas an increase in Pr destabilizes it.