General synthetic iterative scheme for the simulation of rarefied gas flows

ZENG Jianan; ZHANG Yanbing; LI Qi; SU Wei; WU Lei

doi:10.6052/1000-0992-26-007

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Zeng J N, Zhang Y B, Li Q, Su W, Wu L. General synthetic iterative scheme for the simulation of rarefied gas flows. Advances in Mechanics, in press doi: 10.6052/1000-0992-26-007

Citation:

Zeng J N, Zhang Y B, Li Q, Su W, Wu L. General synthetic iterative scheme for the simulation of rarefied gas flows. Advances in Mechanics, in press doi: 10.6052/1000-0992-26-007

Zeng J N, Zhang Y B, Li Q, Su W, Wu L. General synthetic iterative scheme for the simulation of rarefied gas flows. Advances in Mechanics, in press doi: 10.6052/1000-0992-26-007

Citation:

Zeng J N, Zhang Y B, Li Q, Su W, Wu L. General synthetic iterative scheme for the simulation of rarefied gas flows. Advances in Mechanics, in press doi: 10.6052/1000-0992-26-007

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General synthetic iterative scheme for the simulation of rarefied gas flows

doi: 10.6052/1000-0992-26-007 cstr: 32046.14.1000-0992-26-007

ZENG Jianan¹,
ZHANG Yanbing²,
LI Qi³,
SU Wei^{1, 4},
WU Lei^{2
,
,}

1.
Division of Emerging Interdisciplinary Areas, Academy of Interdisciplinary Studies, The Hong Kong University of Science and Technology, Hong Kong SAR, China
2.
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, 518055 Shenzhen, China
3.
School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen, 518107, China
4.
Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong SAR, China

More Information

Corresponding author: wul@sustech.edu.cn
Received Date: 2026-02-06
Accepted Date: 2026-04-02

Available Online: 2026-04-08

Abstract

Abstract

Rarefied gas transport is prevalent in critical fields such as aerospace, vacuum technology, micro- and nano-systems, and inertial confinement fusion. Particularly in extreme processes like spacecraft atmospheric reentry and near-space hypersonic flight, the flow exhibits prominent multiscale characteristics, accompanied by complex multiphysics coupling effects including molecular internal energy excitation, chemical reactions, and radiation. These features significantly increase the complexity of kinetic modeling, leading to severe computational bottlenecks for conventional numerical methods and restricting the accuracy and efficiency of large-scale engineering simulations. To address these challenges, this paper systematically introduces the general synthetic iterative scheme (GSIS), a multiscale numerical method characterized by both fast-convergence and asymptotic-preserving properties. The core of this method lies in the construction of macroscopic synthetic equations that are physically consistent with the kinetic equations. By leveraging the superior information propagation efficiency of parabolic macroscopic systems to guide the evolution of hyperbolic kinetic equations, GSIS breaks the inherent bottleneck where computational grids and time steps are constrained by the molecular collision scales, enabling unified and efficient simulation across all flow regimes. Theoretical analysis and numerical validation demonstrate that GSIS not only rigorously recovers the macroscopic fluid dynamics description in the continuum limit, but also exhibits exceptional iterative convergence efficiency across the entire range of Knudsen numbers. Furthermore, the GSIS framework possesses remarkable model compatibility and algorithmic extensibility. Through a variety of typical benchmarks, this paper highlights its high-precision and high-efficiency performance in problems involving polyatomic gases, high-temperature radiation, multi-component mixtures, and unsteady complex flows. Concurrently, the GSIS mechanism can be deeply integrated with stochastic particle algorithms, achieving significant acceleration of the Boltzmann and Enskog equations within the Direct Simulation Monte Carlo framework. Additionally, this paper presents the recent progress of GSIS in multiscale aerodynamic shape optimization, flow stability analysis, and turbulence-rarefaction interactions, showcasing its promising applications in frontier areas such as transition and turbulence in near-space hypersonic flight. Overall, GSIS provides an essential tool for multiscale numerical simulations of rarefied gas flows, and offers strong theoretical support and practical pathways for high-reliability, high-efficiency engineering simulations and optimization.
- Rarefied gas dynamics,
- Boltzmann equation,
- multiscale methods,
- general synthetic iterative scheme,
- adjoint optimization,
- flow stability

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References(114)

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