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- Alexandre Caboussat, Roland Glowinski, Victoria Pons
- J. Num. Math.
- 2009

— In this article, we address the numerical solution of a non-smooth eigenvalue problem, which has implications in plasticity theory and image processing. The smallest eigenvalue of the non-smooth operator under consideration is shown to be the same for all bounded, sufficiently smooth, domains in two space dimensions. Piecewise linear finite elements are… (More)

A mathematical model for the computation of chemical equilibrium of atmospheric inorganic aerosols is proposed. The equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase and solid salts. A primal-dual method solving the Karush-Kuhn-Tucker conditions is detailed. An active set/Newton method permits… (More)

- N. R. Amundson, A. Caboussat, J. W. He, A. V. Martynenko, V. B. Savarin
- 2005

A new inorganic atmospheric aerosol phase equilibrium model (UHAERO) Abstract. A variety of thermodynamic models have been developed to predict inorganic gas-aerosol equilibrium. To achieve computational efficiency a number of the models rely on a priori specification of the phases present in certain relative humidity regimes. Presented here is a new… (More)

- A. Caboussat, 1 M. Picasso, J. Rappaz

A numerical model for the three-dimensional simulation of liquid-gas flows with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain. In the gas domain, the velocity is disregarded, the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law.… (More)

A general equilibrium model for multiphase multicomponent inorganic atmospheric aerosols is proposed. The thermodynamic equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase and solid salts. A primal-dual algorithm solving the Karush-Kuhn-Tucker conditions is detailed. An active set/Newton method… (More)

A numerical model for the simulation of three-dimensional liquid-gas flows with free surfaces and surface tension is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface… (More)

Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volume-of-fluid method is used for the numerical simulation of two-phase free surface flows involving an incompressible liquid and a… (More)

Mathematical and numerical aspects of free surface flows are investigated. On one hand, the mathematical analysis of some free surface flows is considered. A model problem in one space dimension is first investigated. The Burgers equation with diffusion has to be solved on a space interval with one free extremity. This extremity is unknown and moves in… (More)

A model that rigorously computes the gas-particle partitioning and liquid-liquid equilibrium for organic atmospheric aerosol particles is presented. The dynamics of the mass transfers between the particle and the gas phase are modeled with differential equations and are coupled with a constrained optimization problem for the thermo-dynamic equilibrium… (More)

A numerical method for the computation of the best constant in a Sobolev inequality involving the spaces H 2 (Ω) and C 0 (Ω) is presented. Green's functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with… (More)