Particle hydrodynamics with tessellation techniques

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.Comment: 26 pages, 24 figures, currentversion is accepted by MNRA

Sphere packings II

An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of $R^3$ into polyhedra. The polyhedra are divided into two classes. The first class of polyhedra, called quasi-regular tetrahedra, have density at most that of a regular tetrahedron. The polyhedra in the remaining class have density at most that of a regular octahedron (about 0.7209).Comment: 18 pages. Second of two older papers in the series on the proof of the Kepler conjecture. See math.MG/9811071. The original abstract is preserve

Properties of simulated Milky Way-mass galaxies in loose group and field environments

We test the validity of comparing simulated field disk galaxies with the empirical properties of systems situated within environments more comparable to loose groups, including the Milky Way's Local Group. Cosmological simulations of Milky Way-mass galaxies have been realised in two different environment samples: in the field and in environments with similar properties to the Local Group. Apart from the environments of the galaxies, the samples are kept as homogeneous as possible with equivalent ranges in last major merger time, halo mass and halo spin. Comparison of these two samples allow for systematic differences in the simulations to be identified. Metallicity gradients, disk scale lengths, colours, magnitudes and age-velocity dispersion relations are studied for each galaxy in the suite and the strength of the link between these and environment of the galaxies is studied. The bulge-to-disk ratio of the galaxies show that these galaxies are less spheroid dominated than many other simulated galaxies in literature with the majority of both samples being disk dominated. We find that secular evolution and mergers dominate the spread of morphologies and metallicity gradients with no visible differences between the two environment samples. In contrast with this consistency in the two samples there is tentative evidence for a systematic difference in the velocity dispersion-age relations of galaxies in the different environments. Loose group galaxies appear to have more discrete steps in their velocity dispersion-age relations. We conclude that at the current resolution of cosmological galaxy simulations field environment galaxies are sufficiently similar to those in loose groups to be acceptable proxies for comparison with the Milky Way provided that a similar assembly history is considered.Comment: 16 pages, 11 figures, abstract abridged for arXiv. Accepted for publication in Astronomy & Astrophysic

Highly accurate numerical computation of implicitly defined volumes using the Laplace-Beltrami operator

This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set function. After spatial discretization, local approximation of the hypersurface and application of the Gaussian divergence theorem, the volume integrals are transformed to surface integrals. Application of the surface divergence theorem allows for a further reduction to line integrals which are advantageous for numerical quadrature. We discuss the theoretical foundations and provide details of the numerical algorithm. Finally, we present numerical results for convex and non-convex hypersurfaces embedded in cuboidal domains, showing both high accuracy and thrid- to fourth-order convergence in space.Comment: 25 pages, 17 figures, 3 table