Particle method

In the field of numerical analysis, 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 and vice versa.

History

One of the earliest particle methods is smoothed particle hydrodynamics, presented in 1977.[1] Libersky et al.[2] 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.[3]

In the 1990s a new class of particle methods emerged. The reproducing kernel particle method[4] (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[5] 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.

See also

References
  1. Gingold RA, Monaghan JJ (1977). Smoothed particle hydrodynamics – theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389
  2. Libersky, L.D., Petscheck, A.G., Carney, T.C., Hipp, J.R., Allahdadi, F.A. (1993). High Strain Lagrangian Hydrodynamics. Journal of Computational Physics.
  3. Swegle, J.W., Hicks, D.L., Attaway, S.W. (1995). Smoothed Particle Hydrodynamics Stability Analysis. Journal of Computational Physics. 116(1), 123-134
  4. Liu, W.K., Jun, S., Zhang, Y.F. (1995), Reproducing kernel particle methods, International Journal of Numerical Methods in Fluids. 20, 1081-1106.
  5. 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.

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, ISBN 981-238-456-1.
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