Integer Lattice Dynamics for Vlasov-Poisson

Abstract

We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N^4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.

9 pages, 5 figures, 1 table, mnras

References in corpus (13)

• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• GADGET: A code for collisionless and gasdynamical cosmological simulations
• GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
• TESS: A Relativistic Hydrodynamics Code on a Moving Voronoi Mesh
• The fine-grained phase-space structure of Cold Dark Matter halos
• Streams and caustics: the fine-grained structure of LCDM haloes
• Astrophysical Weighted Particle Magnetohydrodynamics
• Tree-Particle-Mesh: an adaptive, efficient, and parallel code for collisionless cosmological simulation
• An adaptively refined phase-space element method for cosmological simulations and collisionless dynamics
• Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
• A cloudy Vlasov solution
• Direct Simulation Monte Carlo for astrophysical flows: I. Motivation and methodology
• Lattice Stellar Dynamics

Cited by in corpus (4)

• Large-scale dark matter simulations
• On the Schrodinger-Poisson--Vlasov-Poisson correspondence
• Novel Conservative Methods for Adaptive Force Softening in Collisionless and Multi-Species N-Body Simulations
• On the probabilistic approach to the N-body problem