Vlasov versus N-body: the Hénon sphere

Colombi, S.; Sousbie, T.; Peirani, Sébastien; Plum, G.; Suto, Yasushi

doi:10.1093/mnras/stv819

Cited by 20 publications

(32 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For other specific parameters (time step, accuracy of the relative cell-opening criterion, etc. ), we used the same values as those in [18]. Running this Gadget simulation took 205.83 hours on 512 threads of the Center for Computational Astrophysics of the National Astronomical Observatory of Japan.…”

Section: Application To Plasma Physicsmentioning

confidence: 99%

“…for t ∈ [0, 13], the two spheres grow close; the complexity stays steady; 2. for t ∈ [13,16], at the first collision the complexity surges and the kinetic energy makes a jump; 3. for t ∈ [16,18], the spheres recede one from the other; the complexity only increases slowly; 4. for t ∈ [18,30], the spheres interact again; this engenders filamentation phenomenae; 5. for t ∈ [30,40], damping simplifies the solution; the number of points decreases; small scales are dissipated by the numerical scheme at scales close to the local resolution of the grid. The number of points peaks at a maximum of 5, 000, 000, 000 points notwithstanding a small incident at t = 20 without consequences.…”

Section: Application To Plasma Physicsmentioning

confidence: 99%

See 1 more Smart Citation

Six-Dimensional Adaptive Simulation of the Vlasov Equations Using a Hierarchical Basis

Deriaz¹,

Peirani²

2018

Multiscale Model. Simul.

View full text Add to dashboard Cite

Abstract. We present an original adaptive scheme using a dynamically refined grid for the simulation of the six-dimensional Vlasov-Poisson equations. The distribution function is represented in a hierarchical basis that retains only the most significant coefficients. This allows considerable savings in terms of computational time and memory usage. The proposed scheme involves the mathematical formalism of Multiresolution Analysis and computer implementation of Adaptive Mesh Refinement. We apply a finite difference method to approximate the Vlasov-Poisson equations although other numerical methods could be considered. Numerical experiments are presented for the d-dimensional Vlasov-Poisson equations in the full 2d-dimensional phase space for d = 1, 2 or 3. The six-dimensional case is compared to a Gadget N-body simulation.keywords: adaptive mesh refinement, hierarchical basis, wavelet, multiresolution analysis, finite differences, phase-space simulations, Vlasov-Poisson equations 1. Introduction. The general idea of Adaptivity in Numerical Analysis lies in the representation of a complex system by a reduced number of elements. It aims to decrease the computational time and memory resources needed to simulate the system. Often, the situation boils down to a trade-off between a numerical volume (computer memory, number of elementary operations etc.) and an increase in the implementation complexity (data structures or algorithms).The most common adaptive technique used in Mechanics [24,40,45,52,53], Physics [7,42] and Astrophysics [1,59,60] is called the Adaptive Mesh Refinement (AMR). In AMR, a Cartesian grid refines locally into finer Cartesian grids. Such refinement is often associated with finite volume methods [40,52,60]. We can distinguish two different approaches among AMR methods: in patch-based AMR the data structure is a collection of grids of varying sizes and accuracies, which are embedded within each other [42,56], whereas in the fully-threaded tree AMR in which the points or cells, or groups thereof, are stored in the nodes or leaves of a large tree structure [11,36,52,53,60]. We use the latter method.In the present study, we are particularly interested in using adaptive methods to tackle the simulation of large systems. Most of these rely on reduced functional basis discretization. This implicates finite elements where the underlying mesh does not have to be Cartesian [41,55]; wavelets associated with a vast non-linear approximation theory [17]; spectral methods that show a good numerical accuracy [31,51]. The hierarchical bases [7] are special kinds of wavelet bases for which the primal scaling function and the primal wavelet are identical, although their duals remain different. A sparse grid method itself [7,50] is a sub-class of hierarchical bases. It is similar to the hyperbolic -anisotropic-hierarchical base. It allows approximation of highdimensional problems for which there is no medium or high frequency oscillation [10,37]. Tensorization consists of expressing a multi-dimensional function as t...

show abstract

Section: Application To Plasma Physicsmentioning

confidence: 99%

Section: Application To Plasma Physicsmentioning

confidence: 99%

Six-Dimensional Adaptive Simulation of the Vlasov Equations Using a Hierarchical Basis

Deriaz¹,

Peirani²

2018

Multiscale Model. Simul.

View full text Add to dashboard Cite

show abstract

“…Only recently have full 3D3V galactic evolution models been achieved (Yoshikawa et al 2013;Sousbie & Colombi 2016). We mention some previous works based however on smaller dimensionality by Colombi et al (2015) with a detailed bibliography, Alard & Colombi (2005) and also pioneering works to study the stability of galactic discs by Nishida et al (1981) al. (1981).…”

Section: Introductionmentioning

confidence: 99%

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

Bienaymé

2018

A&A

View full text Add to dashboard Cite

We have studied the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carried out the analysis by developing a numerical resolution of the 2D2V (two-dimensional in the physical space, 2D, and two-dimensional in the velocity motion, 2V) collisionless Boltzmann equation (CBE) and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood. We recover similar results to those obtained by other authors using N-body simulations, but we are also able to numerically identify faint structures thanks to the cancelling of the Poisson noise. We find that the ratio of the bar pattern speed to the local circular frequency is in the range Ω B /Ω = 1.77 to 1.91. If the Galactic bar angle orientation is within the range from 24 to 45 degrees, the bar pattern speed is between 46 and 49 km.s −1 .kpc −1 .

show abstract

“…When the particles are non-interactive, one obtains the homogeneous Boltzmann equation, also known as the Vlasov equation [20]. Such description is nearly equivalent to the numerical description of dark matter by means of the N-body simulations, although there are conceptual and quantitative differences in the two approaches [21].…”

Section: Introductionmentioning

confidence: 99%

Description of the evolution of inhomogeneities on a dark matter halo with the Vlasov equation

et al. 2017

View full text Add to dashboard Cite

We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo. Such a collection is assumed to represent a dark matter inhomogeneity which reaches a stationary state determined by the virialization of the system. We describe some features of the stationary states and, by using several halo models, obtain distinctive signatures for the evolution of the inhomogeneities in each of the models.

show abstract

Vlasov versus N-body: the Hénon sphere

Cited by 20 publications

References 49 publications

Six-Dimensional Adaptive Simulation of the Vlasov Equations Using a Hierarchical Basis

Six-Dimensional Adaptive Simulation of the Vlasov Equations Using a Hierarchical Basis

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

Description of the evolution of inhomogeneities on a dark matter halo with the Vlasov equation

Contact Info

Product

Resources

About