TABLE OF CONTENTS / Motivation / Particles versus Continua / Newton's Particle Mechanics / Eulerian and Lagrangian Continuum Mechanics / Microscopic Computer Simulation [Molecular Dynamics] / Statistical Mechanics / Macroscopic Particle Simulation / SPAM /
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Example Problem :
[ Molecular Dynamics Leapfrog and Runge-Kutta Methods ]
The flow of fluids, the deformation of solids, the design of structures able to withstand large and rapid loads, the analysis of complex failure mechanisms all of these require numerical simulation techniques. Typical interesting problems of these types are nonlinear, and often "chaotic" as well, meaning that the evolving numerical solutions are exponentially sensitive to small changes in the initial conditions. SPAM is a simple and flexible numerical technique. It has developed so as to address the need for efficient designs of structures responding to rapid loading and for reliable analyses of fluid and solid flows and deformations.
Smooth Particle Applied Mechanics, "SPAM" for short, is a very general approach to the simulation of bulk matter in motion. Its novelty lies in a clever method for smooth interpolation and differentiation within an irregular grid of moving particles. The emergence of SPAM is a natural consequence of the fast high-capacity computers which make it possible to attack complex numerical problems. Computers feed on algorithms, concrete numerical recipes [1] which can closely approximate the abstract mathematical ideas used to model and to analyze material motion. The last three centuries have seen Newton's analysis of particle motions governed by "action...
