ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conformi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2016-09, Vol.321, p.644-697
Main Authors: Sousbie, Thierry, Colombi, Stéphane
Format: Article
Language:English
Subjects:
ALGORITHMS
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COSMOLOGY
Dark matter
EQUATIONS OF MOTION
HAMILTONIANS
LAGRANGIAN FUNCTION
NONLUMINOUS MATTER
PHASE SPACE
POISSON EQUATION
POTENTIALS
Refinement
Sciences of the Universe
SHEETS
Simplicial mesh
SIMULATION
Tessellation
Vlasov–Poisson
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2016.05.048