Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#

Meshfree and particle methods and their applications

Smoothed Particle Hydrodynamics (SPH) is the most widely established mesh-free method which has been used in several fields as astrophysics, solids mechanics and fluid dynamics. In the particular case of computational fluid dynamics, the model is beginning to reach a maturity that allows carrying out detailed quantitative comparisons with laboratory experiments. Here the state-of-the-art of the classical SPH formulation for free-surface flow problems is described in detail. This is demonstrated using dam-break simulations in 2-D and 3-D. The foundations of the method will be presented using different derivations based on the method of interpolants and on the moving least-squares approach. Different methods to improve the classic SPH approach such as the use of density filters and the corrections of the kernel function and its gradient are examined and tested on some laboratory cases

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J.E. Beraun

Papers

A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems