The Direct Simulation Monte Carlo Method: Going Beyond Continuum Hydrodynamics

Abstract

The Direct Simulation Monte Carlo method is a stochastic, particle-based algorithm for solving kinetic theorys Boltzmann equation. Materials can be modeled at a variety of scales. At the quantum level, for example, time-dependent density functional theory or quantum Monte Carlo may be used. At the atomistic level, typically molecular dynamics is used, while at the continuum level, partial differential equations describe the evolution of conserved quantities and slow variables. Between the atomistic and continuum descriptions lives is the kinetic level. The ability to model at this level is crucial for electron and phonon transport in materials. For classical fluids, especially gases in certain regimes, modeling at this level is required. This article addresses computer simulations at the kinetic level.