A Galerkin-characteristic unified finite element method for moving thermal fronts in porous media

Abstract

We investigate the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non-isothermal flow conditions. The governing equations consist of coupling the Darcy equation for the pressure to two convection–diffusion–reaction equations for the temperature and depth of conversion. The aim is to develop a non-oscillatory unified Galerkin-characteristic method for efficient simulation of moving fronts in porous media. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization of the governing equations. The main feature of the proposed unified finite element method is that the same finite element space is used for all solutions to the problem including the pressure, velocity, temperature and concentration. Analysis of convergence and stability is also presented in this study and error estimates in the L2-norm are established for the numerical solutions. In addition, due to the Lagrangian treatment of convection terms, the standard Courant–Friedrichs–Lewy condition is relaxed and the time truncation errors are reduced in the diffusion–reaction part. We verify the method for the benchmark problem of moving fronts around an array of cylinders. The numerical results obtained demonstrate the ability of the proposed method to capture the main flow features.