Well-posedness and numerical approximation of steady convection-diffusion-reaction problems in porous media

Abstract

We study a class of steady nonlinear convection-diffusion-reaction problems in porous media. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to two equations for the heat and mass transfer. The viscosity and diffusion coefficients are assumed to be nonlinear depending on the temperature and concentration of the medium. Well-posedness of the coupled problem is analyzed and existence along with uniqueness of the weak solution is investigated based on a fixed-point method. An iterative scheme for solving the associated fixed-point problem is proposed and its convergence is studied. Numerical experiments are presented for two examples of coupled convection-diffusion-reaction problems. Applications to radiative heat transfer and propagation of thermal fronts in porous media are also included in this study. The obtained results show good numerical convergence and validate the established theoretical estimates.