Primal-dual interior-point method for thermodynamic gas-particle partitioning

Caboussat, Alexandre

doi:10.1007/s10589-009-9262-5

Cited by 2 publications

(3 citation statements)

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“…Two components systems are constructed by taking pairs of these chemical components. The Gibbs free energy g for organic aerosol particles is modeled by using the UNIFAC model (see [4,6] and references therein for details). This semi-empirical model consists of parametrized functions which account for short and long term interactions between chemical components.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Let us ignore for now that y α and θ α must be positive, and let us eliminate the variables θ α . Starting from a well-chosen initial guess [4,6], the Newton method applied to (5.1) (5.2) consists in computing a displacement in (x α , y α , λ, ζ α ) by solving at each iteration the following linear system (defined by blocks):…”

Section: Primal-dual Interior-point Methodsmentioning

confidence: 99%

“…Besides the macroscopic operators (advection and diffusion), the microscopic processes involve phase transformation and chemical reactions [24,25,26]. The two main processes involving the particle phase are the thermodynamic equilibrium [4,6] inside the particle and the mass transfer between the gas phase and the particle phase [1,9,20].…”

Section: Microscopic Modeling Of Aerosol Particlesmentioning

confidence: 99%

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Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes

Caboussat

2011

Math. Model. Nat. Phenom.

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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.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Primal-dual Interior-point Methodsmentioning

confidence: 99%