**5. Conclusions**

In the present work, the Lattice Boltzmann Method was applied to a problem of the flow of a non-Newtonian Bingham-type fluid between two plates, in the case of a Poiseuille flow.

This method is an alternative to the conventional ones used in computational fluid mechanics, its programming is not complicated, and today it is applied to many engineering problems.

Validations were carried out with the analytical solution of the velocity profiles for the case of a Poiseuille flow and the simulations with Lattice Boltzmann, for the case of Bingham-type fluids, for values of the Bingham number (Bin) of 0.1, 0.2, 0.3, and 0.4. The results of all the simulations were quite acceptable, since the percentage of error between both results did not exceed 2.0%.

The LBM proves to be kind for simulations with small lattices, such as the one used in the present work 64 64. All simulations were performed in a laminar regime.

Three deterministic porous media with porosities of 81.68, 75.75, and 65.82% and nine randomized ones with porosities of 81.62, 73.68, and 65.75% were proposed for three Bingham numbers (0.2, 0.3, and 0.4), to perform all simulations. In them the pressure forces, yield stress, and viscosities were varied.

Profiles of velocities, permeabilities, and local pressures were obtained, in all cases the results and behaviors were acceptable for all porous media, and the three Bingham numbers, although only some of the results obtained, were presented at work.

The LBM with the necessary restrictions allows to perfectly simulate the behavior of fluids, as is the case of the Bingham type; the importance of this is the application of multiple industrial processes, in the displacement of fluids reducing costs and time.

Finally, it would be convenient to perform simulations with turbulent flows to verify the goodness of the method with this type of fluid, in which its description is more complex.
