Numerical limits in the integration of Vlasov-Poisson equation for Cold Dark Matter
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| Main Authors: | , , , , , , , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915233244643328 |
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| author | Cappelli, Luca Murante, Giuseppe Borgani, Stefano Bulgarelli, Andrea Parmiggiani, Nicolò Meneghetti, Massimo Burigana, Carlo Trombetti, Tiziana Sarracino, Giuseppe Testa, Vincenzo Farsian, Farida Rizzo, Alessandro Schillirò, Francesco Cardone, Vincenzo Fabrizio Scaramella, Roberto |
| author_facet | Cappelli, Luca Murante, Giuseppe Borgani, Stefano Bulgarelli, Andrea Parmiggiani, Nicolò Meneghetti, Massimo Burigana, Carlo Trombetti, Tiziana Sarracino, Giuseppe Testa, Vincenzo Farsian, Farida Rizzo, Alessandro Schillirò, Francesco Cardone, Vincenzo Fabrizio Scaramella, Roberto |
| contents | The Vlasov-Poisson systems of equations (VP) describes the evolution of a distribution of collisionless particles under the effect of a collective-field potential. VP is at the basis of the study of the gravitational instability of cosmological density perturbations in Dark-Matter (DM), but its range of application extends to other fields, such as plasma physics.
In the case of Cold Dark Matter, a single velocity is associated with each fluid-element (or particle) , the initial condition presents a stiff discontinuity. This creates problems such as diffusion or negative distribution function when a grid based method is used to solve VP. In this work we want to highlight this problem, focusing on the technical aspects of this phenomenon. By comparing different finite volume methods and a spectral method we observe that, while all integration schemes preserve the invariants of the system (e.g, energy), the physical observable of interest, i.e., the density, is not correctly reproduced. We thus compare the density obtained with the different Eulerian integration schemes with the result obtained from a reference N-body method. We point out that the most suitable method to solve the VP system for a self-gravitating system is a spectral method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_22842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical limits in the integration of Vlasov-Poisson equation for Cold Dark Matter Cappelli, Luca Murante, Giuseppe Borgani, Stefano Bulgarelli, Andrea Parmiggiani, Nicolò Meneghetti, Massimo Burigana, Carlo Trombetti, Tiziana Sarracino, Giuseppe Testa, Vincenzo Farsian, Farida Rizzo, Alessandro Schillirò, Francesco Cardone, Vincenzo Fabrizio Scaramella, Roberto Computational Physics The Vlasov-Poisson systems of equations (VP) describes the evolution of a distribution of collisionless particles under the effect of a collective-field potential. VP is at the basis of the study of the gravitational instability of cosmological density perturbations in Dark-Matter (DM), but its range of application extends to other fields, such as plasma physics. In the case of Cold Dark Matter, a single velocity is associated with each fluid-element (or particle) , the initial condition presents a stiff discontinuity. This creates problems such as diffusion or negative distribution function when a grid based method is used to solve VP. In this work we want to highlight this problem, focusing on the technical aspects of this phenomenon. By comparing different finite volume methods and a spectral method we observe that, while all integration schemes preserve the invariants of the system (e.g, energy), the physical observable of interest, i.e., the density, is not correctly reproduced. We thus compare the density obtained with the different Eulerian integration schemes with the result obtained from a reference N-body method. We point out that the most suitable method to solve the VP system for a self-gravitating system is a spectral method. |
| title | Numerical limits in the integration of Vlasov-Poisson equation for Cold Dark Matter |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2503.22842 |