Efficient simulation of molecular gas transport for micro- and nanoscale applications

Abstract

We describe and validate an efficient method for simulating the Boltzmann transport equation in regimes typically encountered in nanotechnology applications. These transport regimes are characterized by non-vanishing Knudsen numbers, preventing simple analyses based on the Navier-Stokes equations; and also by small departures from equilibrium (low Mach number, small temperature gradients, etc.), which make the traditional particle methods like the direct simulation Monte Carlo (DSMC) computationally inefficient. By considering only the deviation from equilibrium, the low-variance particle method introduced herein, simulates molecular gas transport in near-equilibrium regimes with drastically reduced statistical noise compared to the DSMC method. Compared to previous variance reduction methods, the present approach is able to simulate the more general variable-hard-sphere collision model, which more accurately captures the viscosity dependence on the temperature of real gases, compared to the hard sphere and Bhatnagar-Gross-Krook collision models developed previously. The present formulation uses collision algorithms with no inherent time step error, for improved accuracy. Finally, by using a mass-conservative formulation, accurate simulations can be performed in the transition regime requiring as few as ten particles per cell, which is a drastic improvement over previous approaches and enables efficient simulation of multidimensional problems at arbitrarily small deviation from equilibrium. The new methodology is validated and its capabilities are illustrated by solving a number of benchmark problems. It is subsequently used to evaluate the second-order temperature jump coefficient of a dilute hard sphere gas for the first time.