BackgroundPore-scale modelling is now a well-established progressive research field, which has significantly contributed to fundamental understanding of flow and transport in porous media in the last five decades. Examples can be (and not limited to) reservoir engineering [1][2][3][4], environmental hydrogeology [5], paper and pulp industry [6], fuel cells [7], biology, and medical science [8].The first pore-scale model was developed by Fatt in 1956 [9], who simulated the capillary pressure curve as a function of saturation using a pore-network model. After this legendary work, pore-network models, mainly dominated by quasi-static pore-network models, were developed and applied to reservoir engineering and hydrogeology problems. The pore-network modelling opened up a new horizon in understanding the constitutive relations for two-phase flow such as capillary pressure and relative permeability curves [10,11], and at a later stage exploring the transport phenomena in porous media [12]. With further technological developments in micromodel and X-ray imaging facilities and computational infrastructures, quantitative pore-network models were further developed [13]. Almost all pore-network models for different applications share the common principles: they require analytical or semianalytical solutions for a given specific research problem at the pore scale, meaning that the domain geometry requires to be well defined. That implies that the idealization of pore space to interconnected simplified geometries is inevitable.To alleviate this restriction of pore-network models, direct numerical modelling techniques are employed where the equations are solved numerically on the original pore space without any geometrical idealization. The most commonly used method is lattice Boltzmann (LB) modelling. However, there are several other methods such as smoothed particle hydrodynamics (SPH), level set (LS), volume of fluids (VoF), and density functional method (DFM), which can handle the numerical simulation within the exact geometry.
Focus of this special issueThis special issue presents reviews of three major direct numerical methods, namely LB, SPH, and DFM, to simulate complex processes in porous media. Liu et al. [14] reviewed simulation of single-phase and multiphase multicomponent flow at pore level using the LB method. They reviewed different LB methods, discussed their advantages and disadvantages, and concluded that one method cannot be necessarily the most preferred one. In another review paper by Tartakovsky et al. [15], the SPH method as a Lagrangian method based on a meshless discretization of partial differential equations is discussed. They present the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and they discuss applications of the SPH method for modelling porescale multiphase flows and reactive transport in porous and fractured media. In another review paper by Dinariev and Evseev [16], applications of densit...