Simulations Using Particles

Overview

Motivation: 
Mechanics principles can be used to model phenomena ranging from turbulent fluid flows to biological cell motion. The simulation of such systems requires the development and implementation of numerical methods capable of resolving complex, multi-scale phenomena that evolve in multiscale deforming geometries. In recent years advances in particle methods have lead to the formulation of particle methods capable of simulating such systems across several scales. 

Particle simulations can be formulated by following the motion of interacting particles that carry the mechanical properties of the system under consideration. The simplicity of the method enables modeling of diverse phenomena ranging from deforming tissue to granular flows. In this class we present the fundamental aspects of simulations using particles leading to the development of a multi-scale framework for computational mechanics. 

Content: 
The course will cover, but will not be limited, to the following: Particle simulations of continuum and discrete systems, fast summation algorithms, time integrators, constraints, and multi-resolution. We will present a unifying framework for various particle methods and discuss in this context common elements and differences of techniques such as Smoothed Particle Hydrodynamics, Discrete Element Methods and Molecular Dynamics.