In the above equations, ut and dˆp represent, respectively, the tangential velocity at the bottom boundary and the particle
diameter.
The computational setup employs a channel of size Lx × Ly = 40 × 3. The Cartesian grid in the x- and y-directions
is uniformly spaced with Δx = 0.0392 and Δy = 0.0125. We enforce no-slip conditions everywhere on the boundaries
except for the right wall (at x = Lx) where a non-reflective convective outflow condition of the form