Can you imagine a computational fluid dynamics program that simulates the behavior of different materials separated by well-defined interfaces that are subject to arbitrarily large deformations? Can you also imagine this program capturing shock waves and tracking rarefactions, slip surfaces, and other non-linear hydrodynamic phenomena?

Developing such a program would be a daunting task. You may be surprised to learn that such a program was operating in 1955, long before computer graphics or mechanical pen plotters were available, and even before high-level programming languages like Fortran were popular. Fortran, or Formula Translation System, was proposed by IBM in 1954. The program having these amazing capabilities was a Particle-In-Cell (PIC) method originated by Francis H. Harlow of the Los Alamos National Laboratory (Harlow, F.H., "A Machine Calculation Method for Hydrodynamic Problems," Los Alamos Scientific Laboratory report LAMS-1956, Nov. 1955).

Central to the PIC method is the concept of a Lagrangian particle defined by a location (x,y,z). A particle is said to be Lagrangian when it moves as though it is an element of fluid. The particle may be thought of as the location of the center of mass of the fluid element. In addition to a location, Lagrangian particles are sometimes assigned one or more property values. In the PIC method, for instance, particles have specified masses and a label indicating what material they belong to.

While the underlying computational scheme used in the PIC method employs a fixed Eulerian grid, Lagrangian particles are used to move mass, momentum, and energy through this grid in a way that preserves the identities of the different materials. There are no connections between particles so they are free to move and follow the dynamics of a flow regardless of its complexity.

Paper:

Harlow, F. H., "A Machine Calculation Method for Hydrodynamic Problems," Los Alamos Scientific Laboratory report LAMS-1956 (November 1955).

Another Related Papers:

Harlow, F. H., "A Machine Calculation Method for Hydrodynamic Problems," Los Alamos Scientific Laboratory report LAMS-1956 (November 1955).

Evans, M. W. and Harlow, F. H., "The Particle-in-Cell Method for Hydrodynamic Calculations," Los Alamos Scientific Laboratory report LA-2139 (November 1957).

Harlow, F. H., "Hydrodynamic Problems Involving Large Fluid Distortions," J. Assoc. Comput. Mach. 4,137 (1957).

Evans, M. W. and Harlow, F. H., "Calculation of Supersonic Flow Past an Axially Symmetric Cylinder," J. Aeronaut. Sci. 25, 269 (1958).

Evans, M. W. and Harlow, F. H., "Calculation of Unsteady Supersonic Flow Past a Circular Cylinder," ARS J. 29, 46 (1959).

Harlow, F. H. and Dickman, D. O., "Numerical Study of the Motions of Variously-Shaped Slabs Accelerated by a Hot Gas," Los Alamos Scientific Laboratory report LA-2256 (January 1959).

Harlow, F. H., Dickman, D. O., Harris, D. E., and Martin, R. E., "Two Dimensional Hydrodynamic Calculations," Los Alamos Scientific Laboratory report LA-2301 (September 1959).