A Particle method for stationary transport equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917075391348736 |
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| author | Bailo, Rafael Binard, Julie Degond, Pierre Noble, Pascal |
| author_facet | Bailo, Rafael Binard, Julie Degond, Pierre Noble, Pascal |
| contents | We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles trajectories are computed using the ``time-dependent'' equations, and then the approximation is based on a quadrature method using the particle locations as quadrature points. We prove the convergence of the scheme under suitable regularity assumptions on the data and the solution, together with a ``characteristic completeness'' assumption (the characteristic curves fullfill the whole computational domain). We also provide an error estimate. The scheme is tested numerically on a two dimensional linear equation and we present a numerical study of convergence. Finally, we use this method to carry out numerical simulations of a landscape evolution model, where an erodible topography evolves under the effects of water erosion and sedimentation. The scheme is then useful to deal with wet/dry areas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Particle method for stationary transport equations Bailo, Rafael Binard, Julie Degond, Pierre Noble, Pascal Numerical Analysis We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles trajectories are computed using the ``time-dependent'' equations, and then the approximation is based on a quadrature method using the particle locations as quadrature points. We prove the convergence of the scheme under suitable regularity assumptions on the data and the solution, together with a ``characteristic completeness'' assumption (the characteristic curves fullfill the whole computational domain). We also provide an error estimate. The scheme is tested numerically on a two dimensional linear equation and we present a numerical study of convergence. Finally, we use this method to carry out numerical simulations of a landscape evolution model, where an erodible topography evolves under the effects of water erosion and sedimentation. The scheme is then useful to deal with wet/dry areas. |
| title | A Particle method for stationary transport equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.08774 |