A mathematical model for gas-liquid flows subject to mass transfer and
chemical reactions is presented. It is shown that bubble-induced buoyancy
resembles natural convection and can readily be incorporated into an
incompressible flow solver by using an analog of the Boussinesq
approximation. Extra transport equations with nonlinear source terms
are introduced to describe the evolution of scalar quantities.
A segregated algorithm is proposed for the numerical treatment of
the resulting PDE system. The Navier-Stokes equations are solved by a
projection-like method based on the Pressure Schur Complement approach.
Novel high-resolution finite element schemes of FCT and TVD type are
employed for the discretization of unstable convective terms. Numerical
results for a number of prototypical gas-liquid reactor configurations
illustrate the performance of the developed simulation tools.