Density Estimators in Particle Hydrodynamics: DTFE versus regular SPH

Abstract

We present the results of a study confronting density maps reconstructed by the Delaunay Tessellation Field Estimator (DTFE) and by regular SPH kernel-based techniques. The comparison between the two methods clearly demonstrates the superior performance of the DTFE with respect to conventional SPH methods, in particular at locations where SPH appears to fail. The DTFE is a fully self-adaptive technique for reconstructing continuous density fields from discrete particle distributions, and is based upon the corresponding Delaunay tessellation. Its principal asset is its complete independence of arbitrary smoothing functions and parameters specifying the properties of these. As a result it manages to faithfully reproduce the anisotropies of the local particle distribution and through its adaptive and local nature proves to be optimally suited for uncovering the full structural richness in the density distribution. Through the improvement in local density estimates, calculations invoking the DTFE will yield a much better representation of physical processes which depend on density. The presented results form an encouraging step towards the application and insertion of the DTFE in astrophysical hydrocodes. We describe an outline for the construction of a particle hydrodynamics code in which the DTFE replaces kernel-based methods. Further discussion addresses the issue and possibilities for a moving grid based hydrocode invoking the DTFE, and Delaunay tessellations, in an attempt to combine the virtues of the Eulerian and Lagrangian approaches.

11 pages, 2 figures, accepted for publication in A&A, author info corrected (email addresses added)

References in corpus (6)

• Cosmological SPH simulations: The entropy equation
• The Evolution of X-ray Clusters of Galaxies
• Variable Smoothing Lengths and Energy Conservation in Smoothed Particle Hydrodynamics
• A new method for accurate velocity statistics estimation
• X-ray Clusters of Galaxies as Tracers of Structure in the Universe
• A High-resolution Adaptive Moving Mesh Hydrodynamic Algorithm

Cited by in corpus (24)

• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• Smoothed Particle Hydrodynamics and Magnetohydrodynamics
• ZOBOV: a parameter-free void-finding algorithm
• Initial conditions to cosmological N-body simulations, or how to run an ensemble of simulations
• Tracing the Dark Matter Sheet in Phase Space
• The Cosmic Web: Geometric Analysis
• The Properties of Cosmic Velocity Fields
• A new approach to simulating collisionless dark matter fluids
• VOBOZ: An Almost-Parameter-Free Halo-Finding Algorithm
• Particle hydrodynamics with tessellation techniques
• Numerical estimation of densities
• Weak lensing study of dark matter filaments and application to the binary cluster A 222 and A 223
• Automated detection of filaments in the large scale structure of the universe
• Cosmic velocity--gravity relation in redshift space
• Multi-scale morphology of the galaxy distribution
• Kinematic Morphology of Large-scale Structure: Evolution from Potential to Rotational Flow
• Baryon Pasting Algorithm: Halo-based and Particle-based Pasting Methods
• Galaxy star formation in different environments
• Phase-space structures I: A comparison of 6D density estimators
• Velocity and mass bias in the distribution of dark matter halos
• Straightening the Density-Displacement Relation with a Logarithmic Transform
• Exploring the non-linear density field in the Millennium simulations with tessellations - I. The probability distribution function
• Genus statistics using the Delaunay tessellation field estimation method: (I) tests with the Millennium Simulation and the SDSS DR7
• Gas stripping and mixing in galaxy clusters: A numerical comparison study