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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2512.00685 |
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| _version_ | 1866917285235523584 |
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| author | Mori, Yoichiro Sintavanuruk, Chanoknun Van, Truong-Son P. |
| author_facet | Mori, Yoichiro Sintavanuruk, Chanoknun Van, Truong-Son P. |
| contents | We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a popular approximation in the study of turbulent transport. We prove error estimates in the averaging regime in which the dimensionless relaxation timescale $\varepsilon$ is the small parameter. We show that for any finite time interval, the approximation error is of order $\mathcal{O}(\varepsilon)$ in the strong sense and $\mathcal{O}(\varepsilon^2)$ in the weak sense, whose optimality is checked against computational experiment. Furthermore, we present numerical evidence suggesting that this approximation also captures the long-time behavior of the Langevin dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error analysis of an acceleration corrected diffusion approximation of Langevin dynamics with background flow Mori, Yoichiro Sintavanuruk, Chanoknun Van, Truong-Son P. Probability Numerical Analysis We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a popular approximation in the study of turbulent transport. We prove error estimates in the averaging regime in which the dimensionless relaxation timescale $\varepsilon$ is the small parameter. We show that for any finite time interval, the approximation error is of order $\mathcal{O}(\varepsilon)$ in the strong sense and $\mathcal{O}(\varepsilon^2)$ in the weak sense, whose optimality is checked against computational experiment. Furthermore, we present numerical evidence suggesting that this approximation also captures the long-time behavior of the Langevin dynamics. |
| title | Error analysis of an acceleration corrected diffusion approximation of Langevin dynamics with background flow |
| topic | Probability Numerical Analysis |
| url | https://arxiv.org/abs/2512.00685 |