Author

# Joseph J Monaghan

Other affiliations: Monash University, Clayton campus, University of Cambridge, Max Planck Society

Bio: Joseph J Monaghan is an academic researcher from Monash University. The author has contributed to research in topics: Smoothed-particle hydrodynamics & Angular momentum. The author has an hindex of 52, co-authored 167 publications receiving 29789 citations. Previous affiliations of Joseph J Monaghan include Monash University, Clayton campus & University of Cambridge.

##### Papers published on a yearly basis

##### Papers

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6,206 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: 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.

3,623 citations

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TL;DR: In this paper, the SPH (smoothed particle hydrodynamics) method is extended to deal with free surface incompressible flows, and examples are given of its application to a breaking dam, a bore, the simulation of a wave maker, and the propagation of waves towards a beach.

Abstract: The SPH (smoothed particle hydrodynamics) method is extended to deal with free surface incompressible flows. The method is easy to use, and examples will be given of its application to a breaking dam, a bore, the simulation of a wave maker, and the propagation of waves towards a beach. Arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles. The method is explicit, and the time steps are therefore much shorter than required by other less flexible methods, but it is robust and easy to program.

2,889 citations

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TL;DR: In this article, the particle method SPH is applied to one-dimensional shock tube problems by incorporating an artificial viscosity into the equations of motion, and the results show either excessive oscillation or excessive smearing of the shock front.

Abstract: The particle method SPH is applied to one-dimensional shock tube problems by incorporating an artificial viscosity into the equations of motion. When the artificial viscosity is either a bulk viscosity or the Von Neumann-Richtmyer viscosity, in a form analogous to that for finite differences, the results show either excessive oscillation or excessive smearing of the shock front. The reason for the excessive particle oscillation is that, in the standard form, the artificial viscosity cannot dampen irregular motion on the scale of the particle separation since that scale is usually less than the resolution of the interpolating kernel. We propose a new form of artificial viscosity which eliminates this problem. The resulting shock simulation has negligible oscillation and satisfactorily sharp discontinuities. Results with a gaussian interpolating kernel (with second-order errors) are shown to be greatly inferior to those with a super gaussian kernel (with fourth-order errors).

1,119 citations

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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

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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: 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

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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations