ColDICE: A parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation. (English) Zbl 1349.65551

Sousbie, Thierry; Colombi, Stéphane

J. Comput. Phys. 321, 644-697 (2016).

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 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.

MSC:

65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
45K05	Integro-partial differential equations
65Y05	Parallel numerical computation
76W05	Magnetohydrodynamics and electrohydrodynamics
85-08	Computational methods for problems pertaining to astronomy and astrophysics
85A30	Hydrodynamic and hydromagnetic problems in astronomy and astrophysics

Keywords:

Vlasov-Poisson; tessellation; simplicial mesh; refinement; dark matter; cosmology

Software:

FEAPpv; METIS; ENZO; ParaView; RAMSES; GMWB3D-SLC; CYLGYR; CGAL; MPFR; NBODY6; GADGET; QUALIMUWABA; gmp; MLAPM; AFEM; TreePM; ColDICE; Vador

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