A new model of fluid flow based on the lattice boltzmann method for media with a complex geometric structure

Abstract

Modelling porous media finds its application in many industries and human life, namely from the oil industry and construction to washing dishes. The article considers the processes of filtrating single-phase liquid through a porous structure, the description of which is based on lattice Boltzmann method in two-dimensional space. The problem of taking into account the structure of a simulated porous medium when applying the algorithm of lattice Boltzmann equations has many solutions. Nevertheless, at the microlevel, large errors in approximating the pore boundaries can occur, due to the fact that the lattice sites are assumed to be absolutely liquid or absolutely impenetrable. The paper proposes a model in which the lattice nodes are considered to be partially permeable. Partial permeability in this case refers to having a proportion of solids in the lattice site. As a result, it is possible to derive an equation that obeys the laws of mass and momentum conservation, the validity of which has been proven empirically. Due to the equation symmetry, it can be easily used not only on a plane, but also in three-dimensional space.The new lattice Boltzmann method can be employed, for example, in modelling water filtration through sandy soils, which is used in calculating subsidence of the foundations