A discrete scheme of the fluid motion equation based on the pore-scale SPH method

To study the phenomenon of convection diffusion and solute migration in porous media, the smoothed particle hydrodynamics method is used to solve the N–S equation describing pore water flow and the linear homogeneous second-order differential equation describing the solute diffusion process. The accuracy of the simulation method is verified by solving the one-dimensional definite solution of the convection diffusion equation at a low Peclet (Pe) number. Under the condition of a high Pe number, the simulation experiment of solute breakthrough porous media at the pore scale is simulated. Through the analysis of the velocity distribution of fluid particles in pore channels of porous media and the mechanical dispersion process of solutes in porous media, it is found that the flow velocity presents a parabolic distribution in the pore channel, and the particles with high velocity are mainly concentrated in the middle of the pore channel between the solid particles. The solute dispersion is obvious in porous media, and some fluid particles containing solutes penetrate porous media earlier along fast-flowing pore channels. Finally, the solute breakthrough curve and the motion path length of the particle are obtained through the simulation experiment. The calculation methods of the dispersion degree and tortuosity of porous media are further given, and the dispersion degree of porous media in this paper is 0.000 95 m.