A general synthetic iterative scheme with high-order spatial discretization for rarefied gas mixture flows
Abstract
We develop a high-order discontinuous Galerkin formulation of the general synthetic iterative scheme (GSIS) for steady rarefied gas mixture flows. The resulting GSIS-DG discretizes the mesoscopic kinetic equations for monatomic gas mixtures and the macroscopic synthetic equations with the same polynomial degree and solves them alternately. The kinetic solution supplies nonequilibrium corrections to the stress and heat flux, while the synthetic equations accelerate the convergence toward the steady state. Asymptotic analysis shows that GSIS-DG recovers the continuum limit without requiring the spatial mesh to resolve the molecular mean free path. Numerical results over a wide range of Knudsen numbers demonstrate high-order spatial accuracy and rapid steady-state convergence, with more than an order-of-magnitude reduction in computational cost relative to conventional kinetic iteration in the near-continuum regime. Comparisons with second-order finite-volume GSIS further demonstrate that GSIS-DG achieves comparable or better accuracy on coarser physical meshes with fewer total spatial degrees of freedom.
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BibTeX
@misc{zeng2026general,
title = {{A general synthetic iterative scheme with high-order spatial discretization for rarefied gas mixture flows}},
author = {Jianan Zeng and Wei Su},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04880},
eprint = {2610.04880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04880},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A general synthetic iterative scheme with high-order spatial discretization for rarefied gas mixture flows
AU - Jianan Zeng
AU - Wei Su
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04880
UR - https://arxiv.org/abs/2610.04880
AB - We develop a high-order discontinuous Galerkin formulation of the general synthetic iterative scheme (GSIS) for steady rarefied gas mixture flows. The resulting GSIS-DG discretizes the mesoscopic kinetic equations for monatomic gas mixtures and the macroscopic synthetic equations with the same polynomial degree and solves them alternately. The kinetic solution supplies nonequilibrium corrections to the stress and heat flux, while the synthetic equations accelerate the convergence toward the steady state. Asymptotic analysis shows that GSIS-DG recovers the continuum limit without requiring the spatial mesh to resolve the molecular mean free path. Numerical results over a wide range of Knudsen numbers demonstrate high-order spatial accuracy and rapid steady-state convergence, with more than an order-of-magnitude reduction in computational cost relative to conventional kinetic iteration in the near-continuum regime. Comparisons with second-order finite-volume GSIS further demonstrate that GSIS-DG achieves comparable or better accuracy on coarser physical meshes with fewer total spatial degrees of freedom.
ER -