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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/2508.16564 |
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| _version_ | 1866908499349340160 |
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| author | Galindo-Olarte, Andres Nakao, Joseph Pasha, Mirjeta Qiu, Jing-Mei Taitano, William |
| author_facet | Galindo-Olarte, Andres Nakao, Joseph Pasha, Mirjeta Qiu, Jing-Mei Taitano, William |
| contents | A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a low-rank decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This approach establishes a foundation for extending modern low-rank techniques to solve the Boltzmann equation in realistic settings, particularly where structured representations -- such as conformal geometries -- may not be feasible in practical engineering applications. A nodal discontinuous Galerkin method is employed for spatial discretization, coupled with a low-rank decomposition over the velocity grid, as well as implicit-explicit Runge-Kutta methods for time integration. To handle the limit of vanishing collision time, a multiscale implicit integrator based on an auxiliary moment equation is utilized. The algorithm's order of accuracy, reduced computational complexity, and robustness are demonstrated on a suite of canonical gas kinetics problems with increasing complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Nodal Discontinuous Galerkin Method with Low-Rank Velocity Space Representation for the Multi-Scale BGK Model Galindo-Olarte, Andres Nakao, Joseph Pasha, Mirjeta Qiu, Jing-Mei Taitano, William Numerical Analysis A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a low-rank decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This approach establishes a foundation for extending modern low-rank techniques to solve the Boltzmann equation in realistic settings, particularly where structured representations -- such as conformal geometries -- may not be feasible in practical engineering applications. A nodal discontinuous Galerkin method is employed for spatial discretization, coupled with a low-rank decomposition over the velocity grid, as well as implicit-explicit Runge-Kutta methods for time integration. To handle the limit of vanishing collision time, a multiscale implicit integrator based on an auxiliary moment equation is utilized. The algorithm's order of accuracy, reduced computational complexity, and robustness are demonstrated on a suite of canonical gas kinetics problems with increasing complexity. |
| title | A Nodal Discontinuous Galerkin Method with Low-Rank Velocity Space Representation for the Multi-Scale BGK Model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.16564 |