DETERMINATION OF MACROSCOPIC QUANTITIES FOR A TOWNSEND DISCHARGE IN HELIUM BY BOTH BOLTZMANN EQUATION AND MONTE CARLO METHODS

Monte Carlo Methods for the Linearized Poisson-Boltzmann Equation

We review efficient grid-free random walk methods for solving boundary value problems for the linearized Poisson-Boltzmann equation (LPBE). First we introduce the “Walk On Spheres” (WOS) algorithm [1] for the LPBE. Based on this WOS algorithm, another, related, Monte Carlo algorithm is presented. This modified Monte Carlo method reinterprets the weights used in the original WOS algorithm as sur...

Monte Carlo Methods for Solving the Boltzmann Transport Equation

We review Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons. Our discussion reviews the numerical foundations of Monte Carlo algorithms, basic simulation methodology, as well as recent developments in the field. Examples of the latter include formulations for cal...

Boltzmann Equation Analysis and Monte Carlo Simulation of Electron Transport in N2-O2 streamer discharge

1 Centre for Mathematics and Computer Science (CWI), P.O.Box 94079, 1090 GB Amsterdam, The Netherlands. Phone/FAX: +31-20-592-4164/+31-20-592-4199 E-mail:[email protected] 2 Institute of Physics, University of Belgrade, P.O.Box 68, 11080 Zemun, Belgrade, Serbia. 3 ARC Centre for Antimatter-Matter Studies, School of Engineering and Physical Sciences, James Cook University, 4810 Townsville, QL...

Variance reduction for Monte Carlo solutions of the Boltzmann equation

We show that by considering only the deviation from equilibrium, significant computational savings can be obtained in Monte Carlo evaluations of the Boltzmann collision integral for flow problems in the small Mach number sMad limit. The benefits of this variance reduction approach include a significantly reduced statistical uncertainty when the deviation from equilibrium is small, and a flow-ve...

Investigation of a Discrete Velocity Monte Carlo Boltzmann Equation Solver