1,698 research outputs found
Simulation techniques for cosmological simulations
Modern cosmological observations allow us to study in great detail the
evolution and history of the large scale structure hierarchy. The fundamental
problem of accurate constraints on the cosmological parameters, within a given
cosmological model, requires precise modelling of the observed structure. In
this paper we briefly review the current most effective techniques of large
scale structure simulations, emphasising both their advantages and
shortcomings. Starting with basics of the direct N-body simulations appropriate
to modelling cold dark matter evolution, we then discuss the direct-sum
technique GRAPE, particle-mesh (PM) and hybrid methods, combining the PM and
the tree algorithms. Simulations of baryonic matter in the Universe often use
hydrodynamic codes based on both particle methods that discretise mass, and
grid-based methods. We briefly describe Eulerian grid methods, and also some
variants of Lagrangian smoothed particle hydrodynamics (SPH) methods.Comment: 42 pages, 16 figures, accepted for publication in Space Science
Reviews, special issue "Clusters of galaxies: beyond the thermal view",
Editor J.S. Kaastra, Chapter 12; work done by an international team at the
International Space Science Institute (ISSI), Bern, organised by J.S.
Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke
Hydra: A Parallel Adaptive Grid Code
We describe the first parallel implementation of an adaptive
particle-particle, particle-mesh code with smoothed particle hydrodynamics.
Parallelisation of the serial code, ``Hydra'', is achieved by using CRAFT, a
Cray proprietary language which allows rapid implementation of a serial code on
a parallel machine by allowing global addressing of distributed memory.
The collisionless variant of the code has already completed several 16.8
million particle cosmological simulations on a 128 processor Cray T3D whilst
the full hydrodynamic code has completed several 4.2 million particle combined
gas and dark matter runs. The efficiency of the code now allows parameter-space
explorations to be performed routinely using particles of each species.
A complete run including gas cooling, from high redshift to the present epoch
requires approximately 10 hours on 64 processors.
In this paper we present implementation details and results of the
performance and scalability of the CRAFT version of Hydra under varying degrees
of particle clustering.Comment: 23 pages, LaTex plus encapsulated figure
A multidimensional grid-adaptive relativistic magnetofluid code
A robust second order, shock-capturing numerical scheme for multi-dimensional
special relativistic magnetohydrodynamics on computational domains with
adaptive mesh refinement is presented. The base solver is a total variation
diminishing Lax-Friedrichs scheme in a finite volume setting and is combined
with a diffusive approach for controlling magnetic monopole errors. The
consistency between the primitive and conservative variables is ensured at all
limited reconstructions and the spatial part of the four velocity is used as a
primitive variable. Demonstrative relativistic examples are shown to validate
the implementation. We recover known exact solutions to relativistic MHD
Riemann problems, and simulate the shock-dominated long term evolution of
Lorentz factor 7 vortical flows distorting magnetic island chains.Comment: accepted for publication in Computer Physics Communication
An adaptive grid refinement strategy for the simulation of negative streamers
The evolution of negative streamers during electric breakdown of a
non-attaching gas can be described by a two-fluid model for electrons and
positive ions. It consists of continuity equations for the charged particles
including drift, diffusion and reaction in the local electric field, coupled to
the Poisson equation for the electric potential. The model generates field
enhancement and steep propagating ionization fronts at the tip of growing
ionized filaments. An adaptive grid refinement method for the simulation of
these structures is presented. It uses finite volume spatial discretizations
and explicit time stepping, which allows the decoupling of the grids for the
continuity equations from those for the Poisson equation. Standard refinement
methods in which the refinement criterion is based on local error monitors fail
due to the pulled character of the streamer front that propagates into a
linearly unstable state. We present a refinement method which deals with all
these features. Tests on one-dimensional streamer fronts as well as on
three-dimensional streamers with cylindrical symmetry (hence effectively 2D for
numerical purposes) are carried out successfully. Results on fine grids are
presented, they show that such an adaptive grid method is needed to capture the
streamer characteristics well. This refinement strategy enables us to
adequately compute negative streamers in pure gases in the parameter regime
where a physical instability appears: branching streamers.Comment: 46 pages, 19 figures, to appear in J. Comp. Phy
Block Structured Adaptive Mesh and Time Refinement for Hybrid, Hyperbolic + N-body Systems
We present a new numerical algorithm for the solution of coupled collisional
and collisionless systems, based on the block structured adaptive mesh and time
refinement strategy (AMR). We describe the issues associated with the
discretization of the system equations and the synchronization of the numerical
solution on the hierarchy of grid levels. We implement a code based on a higher
order, conservative and directionally unsplit Godunov's method for
hydrodynamics; a symmetric, time centered modified symplectic scheme for
collisionless component; and a multilevel, multigrid relaxation algorithm for
the elliptic equation coupling the two components. Numerical results that
illustrate the accuracy of the code and the relative merit of various
implemented schemes are also presented.Comment: 40 pages, 10 figures, JPC in press. Extended the code test section,
new convergence tests, several typos corrected. Full resolution version
available at http://www.exp-astro.phys.ethz.ch/miniati/charm.pd
An exact general remeshing scheme applied to physically conservative voxelization
We present an exact general remeshing scheme to compute analytic integrals of
polynomial functions over the intersections between convex polyhedral cells of
old and new meshes. In physics applications this allows one to ensure global
mass, momentum, and energy conservation while applying higher-order polynomial
interpolation. We elaborate on applications of our algorithm arising in the
analysis of cosmological N-body data, computer graphics, and continuum
mechanics problems.
We focus on the particular case of remeshing tetrahedral cells onto a
Cartesian grid such that the volume integral of the polynomial density function
given on the input mesh is guaranteed to equal the corresponding integral over
the output mesh. We refer to this as "physically conservative voxelization".
At the core of our method is an algorithm for intersecting two convex
polyhedra by successively clipping one against the faces of the other. This
algorithm is an implementation of the ideas presented abstractly by Sugihara
(1994), who suggests using the planar graph representations of convex polyhedra
to ensure topological consistency of the output. This makes our implementation
robust to geometric degeneracy in the input. We employ a simplicial
decomposition to calculate moment integrals up to quadratic order over the
resulting intersection domain.
We also address practical issues arising in a software implementation,
including numerical stability in geometric calculations, management of
cancellation errors, and extension to two dimensions. In a comparison to recent
work, we show substantial performance gains. We provide a C implementation
intended to be a fast, accurate, and robust tool for geometric calculations on
polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3
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