Numerical discretization of a Darcy–Forchheimer flow with variable density and heat transfer

In this paper, we study a heat transfer scenario in Darcy–Forchheimer porous media with variable density. The block-centered finite difference method is applied to discretize the non-isothermal flow equations governing the system. Specifically, the pressure field is modeled using the nonlinear Darcy–Forchheimer formulation, while the density and temperature are described by convection-dominated diffusion equations, which are treated via the characteristic method. Theoretical analyses are rigorously developed for pressure, velocity, density, temperature, and auxiliary flux across non-uniform grids. Several numerical experiments are carried out to illustrate the merits of our method by comparing numerical results to analytical solutions.