Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011Complex Fluids
|Page(s)||44 - 66|
|Published online||10 August 2011|
Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes
Department of Mathematics, University of Houston,
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 90C51 / 65N30 / 65K10 / 86A10 / 49M15
Key words: atmospheric flow / air quality / convex envelopes / interior-point method / variational problem / augmented Lagrangian
© EDP Sciences, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.