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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.19624 |
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| _version_ | 1866909864086732800 |
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| author | Wang, Lu Deng, Lingyun Wang, Guanqing Liang, Hong Xu, Jiangrong |
| author_facet | Wang, Lu Deng, Lingyun Wang, Guanqing Liang, Hong Xu, Jiangrong |
| contents | The discrete velocity method (DVM) is a powerful framework for simulating gas flows across continuum to rarefied regimes, yet its efficiency remains limited by existing quadrature rules. Conventional infinite-domain quadratures, such as Gauss-Hermite, distribute velocity nodes globally and perform well near equilibrium but fail under strong nonequilibrium conditions. In contrast, finite-interval quadratures, such as Newton-Cotes, enable local refinement but lose efficiency near equilibrium. To overcome these limitations, we propose a generalized Gauss-Jacobi quadrature (GGJQ) for DVM, built upon a new class of adjustable weight functions. This framework systematically constructs one- to three-dimensional quadratures and maps the velocity space into polar or spherical coordinates, enabling flexible and adaptive discretization. The GGJQ accurately captures both near-equilibrium and highly rarefied regimes, as well as low- and high-Mach flows, achieving superior computational efficiency without compromising accuracy. Numerical experiments over a broad range of Knudsen numbers confirm that GGJQ consistently outperforms traditional Newton-Cotes and Gauss-Hermite schemes, offering a robust and efficient quadrature strategy for multiscale kinetic simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Gauss-Jacobi rules for discrete velocity method in Multiscale Flow Simulations Wang, Lu Deng, Lingyun Wang, Guanqing Liang, Hong Xu, Jiangrong Fluid Dynamics The discrete velocity method (DVM) is a powerful framework for simulating gas flows across continuum to rarefied regimes, yet its efficiency remains limited by existing quadrature rules. Conventional infinite-domain quadratures, such as Gauss-Hermite, distribute velocity nodes globally and perform well near equilibrium but fail under strong nonequilibrium conditions. In contrast, finite-interval quadratures, such as Newton-Cotes, enable local refinement but lose efficiency near equilibrium. To overcome these limitations, we propose a generalized Gauss-Jacobi quadrature (GGJQ) for DVM, built upon a new class of adjustable weight functions. This framework systematically constructs one- to three-dimensional quadratures and maps the velocity space into polar or spherical coordinates, enabling flexible and adaptive discretization. The GGJQ accurately captures both near-equilibrium and highly rarefied regimes, as well as low- and high-Mach flows, achieving superior computational efficiency without compromising accuracy. Numerical experiments over a broad range of Knudsen numbers confirm that GGJQ consistently outperforms traditional Newton-Cotes and Gauss-Hermite schemes, offering a robust and efficient quadrature strategy for multiscale kinetic simulations. |
| title | Generalized Gauss-Jacobi rules for discrete velocity method in Multiscale Flow Simulations |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2510.19624 |