Particle in Cell

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In theoretical physics, the term Particle-in-Cell ( PIC , in English for "particles in a cell") describes a technique for solving certain classes of partial differential equations . The core element is that simulated particles (or elements of a fluid ) are calculated in a continuous phase space in an Euler reference system (so that the equations of motion of the fluid elements can be solved in the form of Euler equations ) . At the same time fields of a distribution of z. B. Densities and currents calculated on Euler's ( stationary ) grid points .

PIC procedure were used as early as 1955, before the availability of the first Fortran - compiler . During the late 1950s and early 1960s the technique gained popularity for plasma simulations by Oscar Buneman , John M. Dawson , Hockney, Birdsall, Morse, and others. a.

Applications

In plasma-physical calculations, the PIC method allows the trajectory of charged particles to be followed in self-consistent electromagnetic (and / or electrostatic ) fields.

It is also used to calculate:

PIC simulations are also used for problems outside of plasma physics, e.g. B. in solid mechanics and fluid mechanics .

Technical aspects

The PIC process can be implemented very intuitively and in a straightforward manner for many problems. This is probably one of the reasons for its success, especially for plasma simulations, which typically involve the following tasks:

In contrast to physical reality, the forces on the particles do not change significantly when they approach each other at distances on the order of fractions of a grid spacing. This can, but need not, be viewed as a problem of the PIC simulation.

Depending on how the forces on the particles are calculated, a distinction is made between different PIC models:

  • PP  ( particle-particle ) model: only the particle-particle interaction is taken into account.
  • PM  ( particle-mesh ) model: only the interactions of the particles with the grid are calculated (simplest case).
  • PP-PM or P 3 M model: takes into account both types of interactions.

Even in the early days of the simulation method was realized that the PIC simulation sensitive to the discrete particles rushing , Eng. discrete particle noise reacts. This error is of a statistical nature, and to this day this type of error remains rather less well understood than the sources of error in traditional approaches that get by with a fixed grid.

A good source for assessing the numerical accuracy of a PIC simulation remains the observation of conserved quantities , in particular the energy .

Individual evidence

  1. ↑ John M. Dawson: Particle simulation of plasmas . In: Reviews of Modern Physics . 55, 1983, p. 403. doi : 10.1103 / RevModPhys.55.403 .
  2. ^ GR Liu, MB Liu: Smoothed Particle Hydrodynamics: A Meshfree Particle Method . World Scientific, 2003, ISBN 981-238-456-1 .
  3. ↑ FH Harlow: The particle-in-cell computing method for fluid dynamics . In: Methods Comput. Phys. . 3, 1964, pp. 319-343.
  4. ↑ Hideo Okuda: nonphysical noises and instabilities in plasma simulation due to a spatial grid . In: Journal of Computational Physics . 10, 1972, p. 475. doi : 10.1016 / 0021-9991 (72) 90048-4 .

literature

  • Charles K. Birdsall, A. Bruce Langdon: Plasma Physics via Computer Simulation . McGraw-Hill, 1985, ISBN 0-07-005371-5 .
  • Roger W. Hockney, James W. Eastwood: Computer Simulation Using Particles . CRC Press, 1988, ISBN 0852743920 .

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