### Abstract

Semi-Lagrangian scheme (cubic polynomial semi-Lagrangian (CSL) or cubic interpolated propagation (CIP) scheme) is applied to condensation equation of cumulative number distribution, and simple correction using mathematical constrains of cumulative number distribution is applied after the semi-Lagrangian procedure at each time step. This solver exactly conserves total particle number N and prevents overshoots of aerosol size distribution with steep gradients. The total surface area S and the total volume V are also easily conserved within small error. In the cases where the size distributions are not extremely sharp, CSL and CIP both can be utilized in the solver for the aerosol condensation. On the other hand, in the cases where the distributions are quite sharp, the solver using CIP gives the almost same result as the exact solution.

Original language | English |
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Pages (from-to) | 1033-1043 |

Number of pages | 11 |

Journal | Aerosol Science and Technology |

Volume | 38 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2004 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Environmental Chemistry
- Materials Science(all)
- Pollution

### Cite this

**A solver for aerosol condensation equation by semi-Lagrangian scheme with correction exactly conserving total particle number.** / Yamamoto, Masaru.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A solver for aerosol condensation equation by semi-Lagrangian scheme with correction exactly conserving total particle number

AU - Yamamoto, Masaru

PY - 2004/10/1

Y1 - 2004/10/1

N2 - Semi-Lagrangian scheme (cubic polynomial semi-Lagrangian (CSL) or cubic interpolated propagation (CIP) scheme) is applied to condensation equation of cumulative number distribution, and simple correction using mathematical constrains of cumulative number distribution is applied after the semi-Lagrangian procedure at each time step. This solver exactly conserves total particle number N and prevents overshoots of aerosol size distribution with steep gradients. The total surface area S and the total volume V are also easily conserved within small error. In the cases where the size distributions are not extremely sharp, CSL and CIP both can be utilized in the solver for the aerosol condensation. On the other hand, in the cases where the distributions are quite sharp, the solver using CIP gives the almost same result as the exact solution.

AB - Semi-Lagrangian scheme (cubic polynomial semi-Lagrangian (CSL) or cubic interpolated propagation (CIP) scheme) is applied to condensation equation of cumulative number distribution, and simple correction using mathematical constrains of cumulative number distribution is applied after the semi-Lagrangian procedure at each time step. This solver exactly conserves total particle number N and prevents overshoots of aerosol size distribution with steep gradients. The total surface area S and the total volume V are also easily conserved within small error. In the cases where the size distributions are not extremely sharp, CSL and CIP both can be utilized in the solver for the aerosol condensation. On the other hand, in the cases where the distributions are quite sharp, the solver using CIP gives the almost same result as the exact solution.

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U2 - 10.1080/027868290524025

DO - 10.1080/027868290524025

M3 - Article

VL - 38

SP - 1033

EP - 1043

JO - Aerosol Science and Technology

JF - Aerosol Science and Technology

SN - 0278-6826

IS - 10

ER -