From Molecular Dynamics to Continuum Models: A Numerical Approach

Byungduck Chough
Carnegie Mellon University, USA

Shlomo Ta'asan
Carnegie Mellon University, USA

Abstract

This talk will describe a numerical approach for the derivation of macroscopic equations (partial differential equations), from simulations of molecular models. Its demonstration will be given for examples starting from the simple Brownian motion to more complex fluid models such as the hard sphere (HS) and Lennard-Jones (LJ) models. The resulting fluid dynamics equations and their deviation from Navier-Stokes equations, especially in the rarefied gas regime, will be discussed. The main component of the method are coloring schemes which track properties such as mass momentum and energy and their dynamics for a collection of particles over proper space and time scales, and deducing their dynamics on the larger scales by regression analysis. These schemes allow the construction of a hierarchy of models describing the phenomenon at different space-time scales. It can be used also for accelerating molecular dynamics computation by exploiting their multiscale structure.