Smoothed particle hydrodynamics.
TL;DR: In this paper, the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed, focusing on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.
Abstract: In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.
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TL;DR: GADGET-2 as mentioned in this paper is a massively parallel tree-SPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics.
Abstract: We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.
6,196 citations
Cites background or methods from "Smoothed particle hydrodynamics."
...This is done by multiplying the viscous tensor with (fi + fj)/2, where fi = |∇ × v|i |∇ · v|i + |∇ × v|i (17) is a simple measure for the relative amount of shear in the flow around particle i, based on standard SPH estimates for divergence and curl (Monaghan, 1992)....
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...Smoothed particle hydrodynamics (SPH) uses a set of discrete tracer particles to describe the state of a fluid, with continuous fluid quantities being defined by a kernel interpolation technique (Lucy, 1977; Gingold & Monaghan, 1977; Monaghan, 1992)....
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TL;DR: In this article, the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed, focusing on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.
Abstract: In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.
4,070 citations
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.
Abstract: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.
3,082 citations
TL;DR: In this paper, a coarse-grained representation of the properties of the interstellar medium (ISM) and BH accretion starting from basic physical assumptions is proposed to incorporate feedback from star formation and black hole accretion into simulations of isolated and merging galaxies.
Abstract: We describe techniques for incorporating feedback from star formation and black hole (BH) accretion into simulations of isolated and merging galaxies. At present, the details of these processes cannot be resolved in simulations on galactic scales. Our basic approach therefore involves forming coarse-grained representations of the properties of the interstellar medium (ISM) and BH accretion starting from basic physical assumptions, so that the impact of these effects can be included on resolved scales. We illustrate our method using a multiphase description of star-forming gas. Feedback from star formation pressurizes highly overdense gas, altering its effective equation of state (EOS). We show that this allows the construction of stable galaxy models with much larger gas fractions than possible in earlier numerical work. We extend the model by including a treatment of gas accretion onto central supermassive BHs in galaxies. Assuming thermal coupling of a small fraction of the bolometric luminosity of accreting BHs to the surrounding gas, we show how this feedback regulates the growth of BHs. In gas-rich mergers of galaxies, we observe a complex interplay between starbursts and central active galactic nuclei (AGN) activity when the tidal interaction triggers intense nuclear inflows of gas. Once an accreting supermassive BH has grown to a critical size, feedback terminates its further growth and expels gas from the central region in a powerful quasar-driven wind. Our simulation methodology is therefore able to address the coupled processes of gas dynamics, star formation and BH accretion during the formation of galaxies.
2,019 citations
Cites methods from "Smoothed particle hydrodynamics."
...For the hydrodynamics, we employ a smoothed particle hydrodynamics (SPH) code which represents fluids elements by particles (Lucy, 1977; Gingold & Monaghan, 1977; Monaghan, 1992)....
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TL;DR: In this paper, a coarse-grained representation of the properties of the interstellar medium and black hole accretion starting from basic physical assumptions is proposed, and the impact of these effects can be included on resolved scales.
Abstract: We describe techniques for incorporating feedback from star formation and black hole accretion into simulations of isolated and merging galaxies. At present, the details of these processes cannot be resolved in simulations on galactic scales. Our basic approach therefore involves forming coarse-grained representations of the properties of the interstellar medium and black hole accretion starting from basic physical assumptions, so that the impact of these effects can be included on resolved scales. We illustrate our method using a multiphase description of star-forming gas. Feedback from star formation pressurises highly overdense gas, altering its effective equation of state. We show that this allows the construction of stable galaxy models with much larger gas fractions than possible in earlier numerical work. We extend the model by including a treatment of gas accretion onto central supermassive black holes in galaxies. Assuming thermal coupling of a small fraction of the bolometric luminosity of accreting black holes to the surrounding gas, we show how this feedback regulates the growth of black holes. In gas-rich mergers of galaxies, we observe a complex interplay between starbursts and central AGN activity when the tidal interaction triggers intense nuclear inflows of gas. Once an accreting supermassive black hole has grown to a critical size, feedback terminates its further growth, and expels gas from the central region in a powerful quasar-driven wind. Our simulation methodology is therefore able to address the coupled processes of gas dynamics, star formation, and black hole accretion during the formation of galaxies.
1,986 citations