A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917225432088576 |
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| author | Himanshi Theisen, Lambert Rana, Anirudh Singh Torrilhon, Manuel Gupta, Vinay Kumar |
| author_facet | Himanshi Theisen, Lambert Rana, Anirudh Singh Torrilhon, Manuel Gupta, Vinay Kumar |
| contents | In this work, we explore the method of fundamental solutions (MFS) for solving the regularized 13-moment (R13) equations for rarefied monatomic gases. While previous applications of the MFS in rarefied gas flows relied on problem-specific fundamental solutions, we propose a generic approach that systematically computes the fundamental solutions for any linear moment system without predefined source terms. The generalized framework is first introduced using a simple example involving the Stokes equations, and is then extended to the R13 equations. The results obtained from the generic MFS are validated against an analytical solution for the R13 equations. Following validation, the framework is applied to the case of thermally-induced flow between two non-coaxial cylinders. Since no analytical solution exists for this case, we compare the results obtained from the MFS with those obtained from the finite element method (FEM). To further assess computational efficiency, we analyze the runtimes of the FEM and MFS. The results indicate that the MFS converges faster than the FEM and serves as a promising alternative to conventional meshing-based techniques. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows Himanshi Theisen, Lambert Rana, Anirudh Singh Torrilhon, Manuel Gupta, Vinay Kumar Fluid Dynamics Mathematical Physics In this work, we explore the method of fundamental solutions (MFS) for solving the regularized 13-moment (R13) equations for rarefied monatomic gases. While previous applications of the MFS in rarefied gas flows relied on problem-specific fundamental solutions, we propose a generic approach that systematically computes the fundamental solutions for any linear moment system without predefined source terms. The generalized framework is first introduced using a simple example involving the Stokes equations, and is then extended to the R13 equations. The results obtained from the generic MFS are validated against an analytical solution for the R13 equations. Following validation, the framework is applied to the case of thermally-induced flow between two non-coaxial cylinders. Since no analytical solution exists for this case, we compare the results obtained from the MFS with those obtained from the finite element method (FEM). To further assess computational efficiency, we analyze the runtimes of the FEM and MFS. The results indicate that the MFS converges faster than the FEM and serves as a promising alternative to conventional meshing-based techniques. |
| title | A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2504.18261 |