### Abstract

A new, accelerated algorithm for a system of elastic hard spheres in which one of the particles (a colloid) is significantly heavier than the others is presented. The algorithm follows the framework of the stochastic heterogeneous multiscale method. In the limit in which the ratio between the light and the heavy particles approaches zero, the dynamics of the colloid is given by a stochastic differential equation whose drift and diffusion coefficients are not known explicitly. It is shown that these coefficients can be calculated on the fly using short-time event-driven simulations, thereby allowing us to simulate the stochastic differential equation for the colloid. The efficiency of the resulting scheme is independent of the mass ratio. A few numerical examples, which serve as a proof of principle, are presented. The examples demonstrate that our results are consistent with analytical predictions in the ideal gas limit. A result of a simulation with a dense gas is also presented.

Original language | English (US) |
---|---|

Pages (from-to) | 349-361 |

Number of pages | 13 |

Journal | Multiscale Modeling and Simulation |

Volume | 7 |

Issue number | 1 |

State | Published - 2008 |

### Fingerprint

### Keywords

- Averaging theorem
- Colloids
- Elastic collisions
- Hard spheres
- Heterogeneous multiscale methods
- Multiscale algorithm
- Stochastic simulation

### ASJC Scopus subject areas

- Modeling and Simulation
- Chemistry(all)
- Computer Science Applications
- Ecological Modeling
- Physics and Astronomy(all)

### Cite this

*Multiscale Modeling and Simulation*,

*7*(1), 349-361.

**Accelerated simulation of a heavy particle in a gas of elastic spheres.** / Ariel, Gil; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

*Multiscale Modeling and Simulation*, vol. 7, no. 1, pp. 349-361.

}

TY - JOUR

T1 - Accelerated simulation of a heavy particle in a gas of elastic spheres

AU - Ariel, Gil

AU - Vanden Eijnden, Eric

PY - 2008

Y1 - 2008

N2 - A new, accelerated algorithm for a system of elastic hard spheres in which one of the particles (a colloid) is significantly heavier than the others is presented. The algorithm follows the framework of the stochastic heterogeneous multiscale method. In the limit in which the ratio between the light and the heavy particles approaches zero, the dynamics of the colloid is given by a stochastic differential equation whose drift and diffusion coefficients are not known explicitly. It is shown that these coefficients can be calculated on the fly using short-time event-driven simulations, thereby allowing us to simulate the stochastic differential equation for the colloid. The efficiency of the resulting scheme is independent of the mass ratio. A few numerical examples, which serve as a proof of principle, are presented. The examples demonstrate that our results are consistent with analytical predictions in the ideal gas limit. A result of a simulation with a dense gas is also presented.

AB - A new, accelerated algorithm for a system of elastic hard spheres in which one of the particles (a colloid) is significantly heavier than the others is presented. The algorithm follows the framework of the stochastic heterogeneous multiscale method. In the limit in which the ratio between the light and the heavy particles approaches zero, the dynamics of the colloid is given by a stochastic differential equation whose drift and diffusion coefficients are not known explicitly. It is shown that these coefficients can be calculated on the fly using short-time event-driven simulations, thereby allowing us to simulate the stochastic differential equation for the colloid. The efficiency of the resulting scheme is independent of the mass ratio. A few numerical examples, which serve as a proof of principle, are presented. The examples demonstrate that our results are consistent with analytical predictions in the ideal gas limit. A result of a simulation with a dense gas is also presented.

KW - Averaging theorem

KW - Colloids

KW - Elastic collisions

KW - Hard spheres

KW - Heterogeneous multiscale methods

KW - Multiscale algorithm

KW - Stochastic simulation

UR - http://www.scopus.com/inward/record.url?scp=55349089952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55349089952&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:55349089952

VL - 7

SP - 349

EP - 361

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 1

ER -