Numerical limits in the integration of Vlasov-Poisson equation for Cold Dark Matter

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: 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
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915233244643328
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
id 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