(4)
where v is the fluid velocity, k is the matrix permeability, μf is the fluid viscosity, p is the fluid pressure, ρf is the fluid density, g is the magnitude of gravitational acceleration, and Z is the position height. Given the boundary conditions, the fluid pressure field can be calculated using Eq. (4), and the corresponding water velocity can be determined using Eq. (3).

2.3 Fluid–Particle Interaction Force

The fluid–solid interaction follows the numerical analysis system of the coarse-grid approach (Tsuji et al., 1993), as shown in Fig. 2. In the coarse-grid method, equations describing the fluid flow are solved numerically on a set of elements that are larger than the particles. The force applied by the fluid to the particles (the fluid–particle interaction force), ffluid , comprises two parts: a drag force and a force due to the fluid pressure gradient, which are given in Eq. (5).