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Mathematical Modeling of Atmospheric Flow and Computation ofConvex Envelopes

Published online by Cambridge University Press:  10 August 2011

A. Caboussat
A. Caboussat*
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3008, USA
*
⋆ Corresponding author. E-mail: caboussat@math.uh.edu
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Abstract

Atmospheric flow equations govern the time evolution of chemical concentrations in theatmosphere. When considering gas and particle phases, the underlying partial differentialequations involve advection and diffusion operators, coagulation effects, and evaporationand condensation phenomena between the aerosol particles and the gas phase. Operatorsplitting techniques are generally used in global air quality models. When consideringorganic aerosol particles, the modeling of the thermodynamic equilibrium of each particleleads to the determination of the convex envelope of the energy function. Two strategiesare proposed to address the computation of convex envelopes. The first one is based on aprimal-dual interior-point method, while the second one relies on a variationalformulation, an appropriate augmented Lagrangian, an Uzawa iterative algorithm, and finiteelement techniques. Numerical experiments are presented for chemical systems ofatmospheric interest, in order to compute convex envelopes in various spacedimensions.

Keywords

atmospheric flowair qualityconvex envelopesinterior-point methodvariational problemaugmented Lagrangian
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 44 - 66
Copyright
© EDP Sciences, 2011

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