In the field of
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
, particle methods discretize fluid into particles. Particle methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort.
Some of particle methods are
meshfree methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original ...
and vice versa.
History
One of the earliest particle methods is
smoothed particle hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysica ...
, presented in 1977. Libersky ''et al.'' were the first to apply SPH in solid mechanics. The main drawbacks of SPH are inaccurate results near boundaries and tension instability that was first investigated by Swegle.
In the 1990s a new class of particle methods emerged. The
reproducing kernel particle method
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original ...
(RKPM) emerged, the approximation motivated in part to correct the kernel estimate in SPH: to give accuracy near boundaries, in non-uniform discretizations, and higher-order accuracy in general. Notably, in a parallel development, the
Material point methods were developed around the same time
[D. Sulsky, Z., Chen, H. Schreyer (1994). a Particle Method for History-Dependent Materials. ''Computer Methods in Applied Mechanics and Engineering'' (118) 1, 179-196.] which offer similar capabilities. During the 1990s and thereafter several other varieties were developed including those listed below.
List of methods and acronyms
The following numerical methods are generally considered to fall within the general class of "particle" methods. Acronyms are provided in parentheses.
*
Smoothed particle hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysica ...
(SPH) (1977)
*
Dissipative particle dynamics Dissipative particle dynamics (DPD) is an off-lattice mesoscopic simulation technique which involves a set of particles moving in continuous space and discrete time. Particles represent whole molecules or fluid regions, rather than single atoms, and ...
(DPD) (1992)
*
Reproducing kernel particle method
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original ...
(RKPM) (1995)
*
Moving particle semi-implicit The moving particle semi-implicit (MPS) method is a computational method for the simulation of incompressible free surface flows. It is a macroscopic, deterministic particle method (Lagrangian mesh-free method) developed by Koshizuka and Oka (1996) ...
(MPS)
*
Particle-in-cell
In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous ph ...
(PIC)
*
Moving particle finite element method
Moving or Movin' may refer to:
Moving of goods
* Relocation (personal), the process of leaving one dwelling and settling in another
* Relocation of professional sports teams
* Relocation (computer science)
* Structure relocation
Music Album ...
(MPFEM)
*
Cracking particles method
Cracking may refer to:
* Cracking, the formation of a fracture or partial fracture in a solid material studied as fracture mechanics
** Performing a sternotomy
* Fluid catalytic cracking, a catalytic process widely used in oil refineries for crack ...
(CPM) (2004)
*
Immersed particle method
Immersion may refer to:
The arts
* "Immersion", a 2012 story by Aliette de Bodard
* ''Immersion'', a French comic book series by Léo Quievreux
* ''Immersion'' (album), the third album by Australian group Pendulum
* ''Immersion'' (film), a 2021 ...
(IPM) (2006)
See also
*
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such ...
*
Boundary element method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, e ...
*
Immersed boundary method
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the flu ...
*
Stencil code
Iterative Stencil Loops (ISLs) are a class of numerical data processing solution
Roth, Gerald et al. (1997)
Proceedings of SC'97: High Performance Networking and Computing.
Compiling Stencils in High Performance Fortran.'
which update arr ...
*
Meshfree methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original ...
References
Further reading
* Liu MB, Liu GR, Zong Z, AN OVERVIEW ON SMOOTHED PARTICLE HYDRODYNAMICS, INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS Vol. 5 Issue: 1, 135–188, 2008.
* Liu, G.R., Liu, M.B. (2003). ''Smoothed Particle Hydrodynamics, a meshfree and Particle Method'', World Scientific, .
External links
Particle Methods
{{DEFAULTSORT:Particle Method
Numerical analysis
Numerical differential equations
Computational fluid dynamics