An Impulse-formed Navier-Stokes Solver based on Long-range Particle Flow Maps
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914297963085824 |
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| author | Li, Zhiqi Chen, Duowen Zhou, Junwei Wang, Sinan Sun, Yuchen Zhu, Bo |
| author_facet | Li, Zhiqi Chen, Duowen Zhou, Junwei Wang, Sinan Sun, Yuchen Zhu, Bo |
| contents | We present a particle-grid characteristic-mapping framework that extends long-range characteristic mapping from inviscid flows to general Navier-Stokes dynamics with viscosity, body forces, and complex boundaries. Unlike traditional grid-based and vorticity-centered characteristic methods, our method is built on the observation that particle trajectories naturally provide the long-range flow map, enabling geometric quantities and their gradients to be transported in a direct and effective manner. We identify the impulse, the gauge variable of the velocity field, as the primary quantity mapped along characteristics while remaining compatible with standard velocity-based incompressible solvers. Using the 1-form representation of the impulse equation, we derive an integral formulation that decomposes the impulse evolution into a component transported geometrically along the particle flow map and a complementary component generated by viscosity and body forces evaluated through path integrals accumulated along particle trajectories. These components together yield a unified characteristic-mapping solver capable of handling incompressible Navier-Stokes flows with viscosity and body forces while maintaining the accuracy and geometric fidelity of characteristic transport. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00499 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Impulse-formed Navier-Stokes Solver based on Long-range Particle Flow Maps Li, Zhiqi Chen, Duowen Zhou, Junwei Wang, Sinan Sun, Yuchen Zhu, Bo Computational Engineering, Finance, and Science We present a particle-grid characteristic-mapping framework that extends long-range characteristic mapping from inviscid flows to general Navier-Stokes dynamics with viscosity, body forces, and complex boundaries. Unlike traditional grid-based and vorticity-centered characteristic methods, our method is built on the observation that particle trajectories naturally provide the long-range flow map, enabling geometric quantities and their gradients to be transported in a direct and effective manner. We identify the impulse, the gauge variable of the velocity field, as the primary quantity mapped along characteristics while remaining compatible with standard velocity-based incompressible solvers. Using the 1-form representation of the impulse equation, we derive an integral formulation that decomposes the impulse evolution into a component transported geometrically along the particle flow map and a complementary component generated by viscosity and body forces evaluated through path integrals accumulated along particle trajectories. These components together yield a unified characteristic-mapping solver capable of handling incompressible Navier-Stokes flows with viscosity and body forces while maintaining the accuracy and geometric fidelity of characteristic transport. |
| title | An Impulse-formed Navier-Stokes Solver based on Long-range Particle Flow Maps |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2602.00499 |