Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media

Abstract

We present an iterative scheme for the numerical analysis of propagating reaction front problems in porous media satisfying an Arrhenius-type law. The governing equations consist of the Darcy equations for the pressure and flow field coupled to two convection–diffusion–reaction equations for the temperature and depth of conversion. Well-posedness, existence and uniqueness of the weak solution are first studied using a fixed-point approach and then, analysis of the proposed iterative scheme is investigated. Numerical results are also presented in order to validate the theoretical estimates and to illustrate the performance of the proposed scheme. The obtained results are in line with our expectations for a good numerical resolution with high accuracy and stability behaviors.