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<ref>R. A. Gingold and J. J. Monaghan "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society '''181''' pp. 375–389 (1977)</ref> in 1977 for astrophysical applications, and has since been applied to many challenging problems in fluid and solid mechanics.  The main advantage of smooth-particle methods is that the partial differential equations (continuity, motion, energy) are replaced by ordinary differential equations (like [[molecular dynamics]]) describing the motion of particles.  The particles can be of any size, from the microscopic to the astrophysical, and can obey any chosen constitutive equation.  The main disadvantages are the difficulties in treating sharp surfaces or interfaces with discrete particles and in avoiding the instabilities that can result for materials under tension.
<ref>R. A. Gingold and J. J. Monaghan "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society '''181''' pp. 375–389 (1977)</ref> in 1977 for astrophysical applications, and has since been applied to many challenging problems in fluid and solid mechanics.  The main advantage of smooth-particle methods is that the partial differential equations (continuity, motion, energy) are replaced by ordinary differential equations (like [[molecular dynamics]]) describing the motion of particles.  The particles can be of any size, from the microscopic to the astrophysical, and can obey any chosen constitutive equation.  The main disadvantages are the difficulties in treating sharp surfaces or interfaces with discrete particles and in avoiding the instabilities that can result for materials under tension.


Some works have been able to link this technique and [[dissipative particle dynamics|DPD]], thus creating the "SDPD method"
Some works have been able to link this technique and [[dissipative particle dynamics|DPD]]
<ref> [http://dx.doi.org/10.1103/PhysRevE.67.026705 Pep Español and Mariano Revenga "Smoothed dissipative particle dynamics", Physical Review E '''67''' p. 026705 (2003) ] </ref>. [[Voronoi particles| Other approach]] is to establish the volume of a particle as the volume of its [[Voronoi_cells| Voronoi_cell]].
<ref> [http://dx.doi.org/10.1103/PhysRevE.67.026705 Pep Español and Mariano Revenga "Smoothed dissipative particle dynamics", Physical Review E '''67''' p. 026705 (2003) ] </ref>.
==References==
==References==
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