Numerical simulation on staggered grids of three-dimensional brinkman-forchheimer flow and heat transfer in porous media

In this paper, three-dimensional numerical algorithm is constructed to simulate the behavior of the Brinkman-Forchheimer flow and thermal fields. Numerical results of velocity, pressure and temperature are obtained by applying the efficient modified two-grid marker and cell (MAC) algorithm on staggered grids with the second-order backward difference formula (BDF2) time approximation. The modified-upwind idea is introduced to convective heat transfer equations for improving accuracy without any numerical oscillation. The second-order convergence rate can be achieved for pressure, velocity and temperature of considered three-dimensional model. Some numerical experiments are presented to illustrate the efficiency of algorithm. The numerical example with analytical solution is used to validate the effectiveness and accuracy of the algorithm by comparing with the results of traditional MAC algorithm. A time-dependent test is proposed to show a detailed sensitivity analysis to indicate the influence of parameters including the \(\varepsilon \) $\epsilon$ , Forchheimer number, Brinkman number and thermal diffusivity on the physical properties of Brinkman-Forchheimer flow and heat transfer in porous media.