Numerical simulation of the flow in a two-layer porous channel by the lattice Boltzmann method

We have numerically investigated the flow of a viscous fluid in a gravitational field within an inclined two-layer channel of finite width, half-filled with a porous medium. The simulation was carried out over a wide range of Darcy and Reynolds numbers. The porosity coefficient of the medium was assumed to be homogeneous and constant. The problem was solved using the lattice Boltzmann method. The representative elementary volume (REV) method was used to simulate the flow in the porous medium. To verify the numerical scheme, two types of boundary conditions were applied at the upper boundary: a solid boundary and a free non-deformable boundary. As the study shows, the method accurately reproduces the flow characteristics for a given porosity coefficient, demonstrating strong agreement with results obtained using the finite difference method. An increase in the channel width leads to a more intense flow, reflected in the growth of the Reynolds number, and with further expansion the Kelvin–Helmholtz instability develops.