Conservative, special-relativistic smoothed particle hydrodynamics

Journal Article · Mon Nov 01 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.08.002· OSTI ID:21418117

Rosswog, Stephan ^[1]

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1. School of Engineering and Science, Jacobs University Bremen, 28759 Bremen (Germany)

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 the terms that stem from non-constant smoothing lengths, usually called '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. As expected for a Lagrangian method, it 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.

• OSTI ID: 21418117
• Journal Information: Journal of Computational Physics, Vol. 229, Issue 22; Other Information: DOI: 10.1016/j.jcp.2010.08.002; PII: S0021-9991(10)00439-0; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ADVECTION
BARYONS
COMPUTERIZED SIMULATION
EIGENVALUES
EQUATIONS
HYDRODYNAMICS
IDEAL FLOW
LAGRANGIAN FUNCTION
PARTICLE DECAY
PERFORMANCE
RELATIVISTIC RANGE
RELATIVITY THEORY
SHOCK TUBES
VISCOSITY
DECAY
ELEMENTARY PARTICLES
ENERGY RANGE
FERMIONS
FLUID FLOW
FLUID MECHANICS
FUNCTIONS
HADRONS
INCOMPRESSIBLE FLOW
MASS TRANSFER
MECHANICS
SIMULATION
STEADY FLOW