An efficient treatment of heat-flux boundary conditions in GSIS for rarefied gas flows
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914266211155968 |
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| author | Zhang, Yanbing Yuan, Ruifeng Luo, Liyan Wu, Lei |
| author_facet | Zhang, Yanbing Yuan, Ruifeng Luo, Liyan Wu, Lei |
| contents | Heat-flux boundary conditions are challenging to implement efficiently in rarefied gas flow simulations because the wall-reflected gas temperature and density must be determined dynamically during the computation. This paper aims to tackle this problem within the general synthetic iterative scheme (GSIS), where the Boltzmann kinetic equation is solved deterministically in an outer loop and macroscopic synthetic equations are solved in an inner loop. To avoid kinetic-macroscopic boundary-flux mismatch and the resulting convergence bottlenecks, for the macroscopic boundary flux at every inner iteration, the incident increment is estimated using a Maxwellian distribution, and then the reflected contribution is obtained by boundary conditions consistent with those in the kinetic solver. In addition to retaining the fast-converging and asymptotic-preserving properties of GSIS, the proposed method significantly reduces the iterations required to determine the wall-reflected gas parameters. Numerical simulations of rarefied gas flows in and around a 3D nozzle, a 2D adiabatic cylinder, and a 2D annular heat-transfer configuration show good agreement with the direct simulation Monte Carlo method, while achieving substantial efficiency gains over conventional iterative schemes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13870 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An efficient treatment of heat-flux boundary conditions in GSIS for rarefied gas flows Zhang, Yanbing Yuan, Ruifeng Luo, Liyan Wu, Lei Computational Physics Fluid Dynamics Heat-flux boundary conditions are challenging to implement efficiently in rarefied gas flow simulations because the wall-reflected gas temperature and density must be determined dynamically during the computation. This paper aims to tackle this problem within the general synthetic iterative scheme (GSIS), where the Boltzmann kinetic equation is solved deterministically in an outer loop and macroscopic synthetic equations are solved in an inner loop. To avoid kinetic-macroscopic boundary-flux mismatch and the resulting convergence bottlenecks, for the macroscopic boundary flux at every inner iteration, the incident increment is estimated using a Maxwellian distribution, and then the reflected contribution is obtained by boundary conditions consistent with those in the kinetic solver. In addition to retaining the fast-converging and asymptotic-preserving properties of GSIS, the proposed method significantly reduces the iterations required to determine the wall-reflected gas parameters. Numerical simulations of rarefied gas flows in and around a 3D nozzle, a 2D adiabatic cylinder, and a 2D annular heat-transfer configuration show good agreement with the direct simulation Monte Carlo method, while achieving substantial efficiency gains over conventional iterative schemes. |
| title | An efficient treatment of heat-flux boundary conditions in GSIS for rarefied gas flows |
| topic | Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2601.13870 |