(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).