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.