Multiphase smoothed-particle hydrodynamics

We adapt the smoothed-particle hydrodynamics (SPH) technique to allow a multiphase fluid in which SPH particles of widely differing density may be freely intermixed. Applications include modelling of galaxy formation and cooling flows

Smoothed Particle Hydrodynamics and Magnetohydrodynamics

This paper presents an overview and introduction to Smoothed Particle Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several `urban myths' regarding SPH, in particular the idea that one can simply increase the `neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.Comment: 44 pages, 14 figures, accepted to special edition of J. Comp. Phys. on "Computational Plasma Physics". The ndspmhd code is available for download from http://users.monash.edu.au/~dprice/ndspmhd

Smoothed Particle Hydrodynamics

Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on a Lagrangian formulation, which has been widely applied to different areas in astrophysics involving complicated fluid dynamical processes. For the first part of this project we have expanded an existing smoothed particle hydrodynamic code (StarCrash). We have added different time integration methods and used them to study the code\u27s overall ability to conserve energy. In the second part we have evaluated the StarCrash code\u27s ability to use different numerical treatments to perform shock tube simulations via Sod\u27s shock tube test. We have used different evolution schemes involving either the energy or the entropy of the system, along with different artificial viscosity formulations, and compared the results from the numerical simulations with the analytical solution

Conservative, special-relativistic smoothed particle hydrodynamics

We present and test a new, special-relativistic formulation of Smoothed Particle Hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived from the Lagrangian of an ideal fluid and accounts for special-relativistic "grad-h terms". In our approach, we evolve the canonical momentum and the canonical energy per baryon and thus circumvent some of the problems that have plagued earlier formulations of relativistic SPH. We further use a much improved artificial viscosity prescription which uses the extreme local eigenvalues of the Euler equations and triggers selectively on a) shocks and b) velocity noise. The shock trigger accurately monitors the relative density slope and uses it to fine-tune the amount of artificial viscosity that is applied. This procedure substantially sharpens shock fronts while still avoiding post-shock noise. If not triggered, the viscosity parameter of each particle decays to zero. None of these viscosity triggers is specific to special relativity, both could also be applied in Newtonian SPH. The performance of the new scheme is explored in a large variety of benchmark tests where it delivers excellent results. Generally, the grad-h terms deliver minor, though worthwhile, improvements. The scheme performs close to perfect in supersonic advection tests, but also in strong relativistic shocks, usually considered a particular challenge for SPH, the method yields convincing results. For example, due to its perfect conservation properties, it is able to handle Lorentz-factors as large as $\gamma= 50 \; 000$ in the so-called wall shock test. Moreover, we find convincing results in a rarely shown, but challenging test that involves so-called relativistic simple waves and also in multi-dimensional shock tube tests.Comment: 39 pages, 19 figures, Journal of Computational Physics in press, reference upate

Ionizing Radiation in Smoothed Particle Hydrodynamics

A new method for the inclusion of ionizing radiation from uniform radiation fields into 3D Smoothed Particle Hydrodynamics (SPHI) simulations is presented. We calculate the optical depth for the Lyman continuum radiation from the source towards the SPHI particles by ray-tracing integration. The time-dependent ionization rate equation is then solved locally for the particles within the ionizing radiation field. Using test calculations, we explore the numerical behaviour of the code with respect to the implementation of the time-dependent ionization rate equation. We also test the coupling of the heating caused by the ionization to the hydrodynamical part of the SPHI code.Comment: 9 pages, 9 figures. accepted by MNRA