# Smoothed particle hydrodynamics: Theory and application to non-spherical stars

01 Dec 1977-Monthly Notices of the Royal Astronomical Society (Oxford University Press)-Vol. 181, Iss: 3, pp 375-389

About: This article is published in Monthly Notices of the Royal Astronomical Society.The article was published on 1977-12-01 and is currently open access. It has received 6206 citations till now. The article focuses on the topics: Stellar rotation & Smoothed-particle hydrodynamics.

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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 from "Smoothed particle hydrodynamics: Th..."

...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, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.

Abstract: An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.

5,324 citations

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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

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TL;DR: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed and is called the reproducingkernel particle method (RKPM).

Abstract: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.

2,682 citations

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TL;DR: In this article, the authors show that at low z < 1, the cosmic star formation rate degrades due to geometry, as the typical cross section of filaments begins to exceed that of the galaxies at their intersections.

Abstract: Not the way one might have thought. In hydrodynamic simulations of galaxy formation, some gas follows the traditionally envisioned route, shock heating to the halo virial temperature before cooling to the much lower temperature of the neutral ISM. But most gas enters galaxies without ever heating close to the virial temperature, gaining thermal energy from weak shocks and adiabatic compression, and radiating it just as quickly. This “cold mode” accretion is channeled along filaments, while the conventional, “hot mode” accretion is quasi-spherical. Cold mode accretion dominates high redshift growth by a substantial factor, while at z < 1 the overall accretion rate declines and hot mode accretion has greater relative importance. The decline of the cosmic star formation rate at low z is driven largely by geometry, as the typical cross section of filaments begins to exceed that of the galaxies at their intersections.

2,155 citations