Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes

A. Caboussat

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 5, page 44-66
  • ISSN: 0973-5348

Abstract

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Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol particles, the modeling of the thermodynamic equilibrium of each particle leads to the determination of the convex envelope of the energy function. Two strategies are proposed to address the computation of convex envelopes. The first one is based on a primal-dual interior-point method, while the second one relies on a variational formulation, an appropriate augmented Lagrangian, an Uzawa iterative algorithm, and finite element techniques. Numerical experiments are presented for chemical systems of atmospheric interest, in order to compute convex envelopes in various space dimensions.

How to cite

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Caboussat, A.. "Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes." Mathematical Modelling of Natural Phenomena 6.5 (2011): 44-66. <http://eudml.org/doc/222410>.

@article{Caboussat2011,
abstract = {Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol particles, the modeling of the thermodynamic equilibrium of each particle leads to the determination of the convex envelope of the energy function. Two strategies are proposed to address the computation of convex envelopes. The first one is based on a primal-dual interior-point method, while the second one relies on a variational formulation, an appropriate augmented Lagrangian, an Uzawa iterative algorithm, and finite element techniques. Numerical experiments are presented for chemical systems of atmospheric interest, in order to compute convex envelopes in various space dimensions.},
author = {Caboussat, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {atmospheric flow; air quality; convex envelopes; interior-point method; variational problem; augmented Lagrangian},
language = {eng},
month = {8},
number = {5},
pages = {44-66},
publisher = {EDP Sciences},
title = {Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes},
url = {http://eudml.org/doc/222410},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Caboussat, A.
TI - Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/8//
PB - EDP Sciences
VL - 6
IS - 5
SP - 44
EP - 66
AB - Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol particles, the modeling of the thermodynamic equilibrium of each particle leads to the determination of the convex envelope of the energy function. Two strategies are proposed to address the computation of convex envelopes. The first one is based on a primal-dual interior-point method, while the second one relies on a variational formulation, an appropriate augmented Lagrangian, an Uzawa iterative algorithm, and finite element techniques. Numerical experiments are presented for chemical systems of atmospheric interest, in order to compute convex envelopes in various space dimensions.
LA - eng
KW - atmospheric flow; air quality; convex envelopes; interior-point method; variational problem; augmented Lagrangian
UR - http://eudml.org/doc/222410
ER -

References

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