Particle-In-Cell Method Studies and Their Applications

Methods are presented for the numerical solution of boundary value problems in which large displacements are produced in a medium. The particle-in-cell method that uses a combined Eulerian-Lagrangian computational scheme is derived together with an improved sharp-shock particle-in-cell procedure. Whereas the standard approach contains an inherent mechanism for the spreading of sharp discontinuities at wave fronts in the media, the sharp shock modifications allows for the propagation of sharp fronts. The application of both approaches to a series of problems in one dimensional space-time coordinates indicates a significant advantage to the sharp shock approach. Such methods are particularly well suited for application to high velocity impact and cratering problems.