Particle method

A numerical-experimental method for modelling the motion of a continuous or discrete medium. A lot of particle methods use the Euler–Lagrange or the Lagrange description of the motion of a medium. For the solution of the system of equations of motion of a compressible medium, the most widespread is the large-particle method (cf. [1]), used in the investigation of single- and multi-phase homogeneous and heterogeneous flows of gases and liquids. Particle methods include the free-point method (cf. [1], [2]), in which there is no fixed pattern. One of the first incomplete particle methods was the particle-in-cell method (the PIC method, cf. [3]). This uses two calculation grids, the Euler and the Lagrange grid. Because of the discrete representation of continuous media, this method usually gives rise to considerable fluctuations in the solution. To minimize the fluctuation one uses the method of particle-layers in the spatial one-dimensional case. Related to the PIC method is the FLIC method, which has poor dissipative properties (cf. [4]). For calculations on incompressible media one use the MAC (cf. [5]) and SMAC (cf. [6]) methods, in which the particles play the role of markers to distinguish the surface of division between the media. Particle methods have become widespread in the description of turbulence, in the dynamics of dispersing gases, and in the solution of electrodynamic and other problems (cf. [1], [7]).

References

[1]	O.M. Belotserkovskii, Yu.M. Davydov, "The method of large particles in gas dynamics. Numerical experiments" , Moscow (1982) (In Russian)
[2]	V.F. D'yachenko, "A new method for the numerical solution of nonstationary problems of gas dynamics with two spatial variables" USSR Comp. Math. Math. Phys. , 5 : 4 (1965) pp. 133–143 Zh. Vychish. Mat. i Mat. Fiz. , 5 : 4 (1965) pp. 680–688
[3]	M.W. Evans, F.H. Harlow, "The particle-in-cell method for hydrodynamical calculations" , Los Alamos (1957)
[4]	R.A. Gentry, R.E. Martin, B.J. Daly, Comput. Phys. , 1 : 1 (1966) pp. 87–118
[5]	, The MAC-method , Los Alamos (1966)
[6]	A.A. Amsden, F.H. Harlow, "The SMAC-method: a numerical technique for calculating incompressible fluid flows" , Los Alamos (1970)
[7]	Yu.A. Berezin, V.A. Vshivkov, "The particle method in the dynamics of dispersing plasms" , Novosibirsk (1980) (In Russian)