# Low-variance direct Monte Carlo simulations using importance weights

Husain A. Al-Mohssen; Nicolas G. Hadjiconstantinou

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 5, page 1069-1083
- ISSN: 0764-583X

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topAl-Mohssen, Husain A., and Hadjiconstantinou, Nicolas G.. "Low-variance direct Monte Carlo simulations using importance weights." ESAIM: Mathematical Modelling and Numerical Analysis 44.5 (2010): 1069-1083. <http://eudml.org/doc/250772>.

@article{Al2010,

abstract = {
We present an efficient approach for reducing the statistical uncertainty
associated with direct Monte Carlo simulations of the Boltzmann equation.
As with previous variance-reduction approaches, the resulting relative
statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the
characteristic value of quantity of interest) is small
and independent of the magnitude of the deviation from equilibrium,
making the simulation of arbitrarily small deviations from equilibrium
possible. In contrast to previous variance-reduction methods, the
method presented here is able to substantially reduce variance with
very little modification to the standard DSMC algorithm. This is achieved
by introducing an auxiliary equilibrium simulation which, via an importance
weight formulation, uses the same particle data as the non-equilibrium
(DSMC) calculation; subtracting the equilibrium from the non-equilibrium
hydrodynamic fields drastically reduces the statistical uncertainty
of the latter because the two fields are correlated. The resulting formulation
is simple to code and provides considerable computational savings for
a wide range of problems of practical interest. It
is validated by comparing our results with DSMC solutions for steady
and unsteady, isothermal and non-isothermal problems; in all cases
very good agreement between the two methods is found.
},

author = {Al-Mohssen, Husain A., Hadjiconstantinou, Nicolas G.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {DSMC; variance reduction; microscale gas flow; direct simulation Monte Carlo (DSMC); Monte Carlo; Boltzmann equation},

language = {eng},

month = {8},

number = {5},

pages = {1069-1083},

publisher = {EDP Sciences},

title = {Low-variance direct Monte Carlo simulations using importance weights},

url = {http://eudml.org/doc/250772},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Al-Mohssen, Husain A.

AU - Hadjiconstantinou, Nicolas G.

TI - Low-variance direct Monte Carlo simulations using importance weights

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/8//

PB - EDP Sciences

VL - 44

IS - 5

SP - 1069

EP - 1083

AB -
We present an efficient approach for reducing the statistical uncertainty
associated with direct Monte Carlo simulations of the Boltzmann equation.
As with previous variance-reduction approaches, the resulting relative
statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the
characteristic value of quantity of interest) is small
and independent of the magnitude of the deviation from equilibrium,
making the simulation of arbitrarily small deviations from equilibrium
possible. In contrast to previous variance-reduction methods, the
method presented here is able to substantially reduce variance with
very little modification to the standard DSMC algorithm. This is achieved
by introducing an auxiliary equilibrium simulation which, via an importance
weight formulation, uses the same particle data as the non-equilibrium
(DSMC) calculation; subtracting the equilibrium from the non-equilibrium
hydrodynamic fields drastically reduces the statistical uncertainty
of the latter because the two fields are correlated. The resulting formulation
is simple to code and provides considerable computational savings for
a wide range of problems of practical interest. It
is validated by comparing our results with DSMC solutions for steady
and unsteady, isothermal and non-isothermal problems; in all cases
very good agreement between the two methods is found.

LA - eng

KW - DSMC; variance reduction; microscale gas flow; direct simulation Monte Carlo (DSMC); Monte Carlo; Boltzmann equation

UR - http://eudml.org/doc/250772

ER -

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