Multiscale Kinetic Transport
Abstract
We present variance reduction methods for drastically reducing the statistical uncertainty associated with Monte Carlo methods for solving the Boltzmann transport equation. The variance reduction, achieved by simulating the deviation from equilibrium, provides a speedup compared to traditional methods such as direct simulation Monte Carlo (DSMC) which increases quadratically as the deviation from equilibrium goes to zero, thus enabling the simulation of arbitrarily small deviations from equilibrium. We show that in addition to reducing the computational cost associated with simulations, the control variate approach can be used to remove the stiffness associated with reaching the continuum limit. In other words, simulating the deviation from equilibrium endows particle methods with the ability to seamlessly capture both the molecular and the continuum regimes at comparable computational cost.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2011
 DOI:
 10.1063/1.3637811
 Bibcode:
 2011AIPC.1389.1124H
 Keywords:

 simulation;
 NavierStokes equations;
 Monte Carlo methods;
 heat transfer;
 02.60.Cb;
 47.10.ad;
 61.20.Ja;
 44.05.+e;
 Numerical simulation;
 solution of equations;
 NavierStokes equations;
 Computer simulation of liquid structure;
 Analytical and numerical techniques