Adaptive GSIS for rarefied gas flow simulations

Abstract: The parallel solver of the general synthetic iterative scheme (GSIS), as recently developed by Zhang \textit{et. al.} in Comput. Fluids 281 (2024) 106374, is an efficient method to find the solution of the Boltzmann equation deterministically. However, it consumes a significant computational memory due to the discretization of molecular velocity space in hypersonic flows. In this paper, we address this issue by introducing the adaptive GSIS, where the Boltzmann equation is applied only in rarefied regions when the local Knudsen number exceeds a reference value, $\text{Kn}{ref}$. In contrast, the Navier-Stokes equations, with and without the high-order corrections to the constitutive relations, are applied in the continuum and rarefied regimes, respectively. Numerical results indicate that setting $\text{Kn}{ref}=0.01$ yields acceptable outcomes. With the adaptive GSIS, the computational memory and time can be significantly reduced in near-continuum flows, e.g. 24 and 7 times, respectively. in the simulation of rarefied gas flow passing the International Space Station.