# MODELING OF POROUS MEDIA BY THE LATTICE BOLTZMANN METHOD

• A.A. Avramenko Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine
• A.I. Tyrinov Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine
• V.E. Domashev Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine
• A.V. Kovalenko Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine

### Abstract

The principles of modeling heat and mass transfer and hydrodynamics of flows in porous media using the lattices Boltzmann method are considered. The methodology for implementing the Darcy law for the lattices Boltzmann method is shown.

In contrast to traditional numerical schemes based on discretization of continuous medium equations, the lattices Boltzmann method is based on microscopic models and mesoscopic kinetic equations. The fundamental idea of the lattices Boltzmann method is to build such simplified kinetic models that include the existing physics of microscopic or mesoscopic processes so that the macroscopic averaged properties correspond to the required macroscopic equations. The main premise of using this simplified method is that the macroscopic dynamics of a fluid is the result of the collective behavior of many microscopic particles of the system.

There are two approaches to modeling porous media using the lattices Boltzmann method. The first of them consists in modeling the spatial structure of the simulated system. Therefore, no additional factors need to be considered. The second approach is that the integrated characteristics of the porous medium (Darcy and Forheimer laws) are used to take into account the effect of porosity on the flow.

The purpose of this paper is to show the realization of the linear law of hydrodynamic drag (Darcy) in porous media for the lattices Boltzmann method. Usually, the main goal of direct modeling is to determine the integral characteristics of a porous medium.

The work considers the flow of fluid through a porous channel, which is formed between two flat walls. A method for implementing the Darcy law in the lattices Boltzmann method is shown.

This work will help to simulate the heat transfer and hydrodynamics of flows in porous media without the use of commercial packages.

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