The Investigation of the Hydrodynamics of an Artificial Reef - Aquaculture and the Environment: A Shared Destiny - page 83

Here, η = Sk / ε and η 0 and β are constants equal to 4.380 and 0.012, respectively.
2.3 Boundary conditions
The boundaries of the computational domain are categorized as inlet, outlet, and wall. The
mean velocity is specified at the inlet where the turbulent kinetic energy and specific
dissipation rate are calculated according to the computational formulas of the turbulence
parameter. The flow at the outlet is not defined and is allowed to change as the
hydrodynamic pressure at all the boundaries is calculated from inside the domain. A
stationary no-slip boundary condition is prescribed on the flume and artificial reef, and the
undisturbed free surface is treated as a “moving wall”, which has zero shear force and the
same speed as the incoming fluid. For coarse meshes, boundary layers cannot be discretized
in sufficient detail. The standard wall functions based on the proposal of Launder and
Spalding was used to bridge the solution variables in the cell next to the wall to the values at
the wall.
2.4 Meshing
The computational grids are shown in Fig. 1. Meshes for modeling flow fields of artificial
reefs using FLUENT were created in GAMBIT. In this work, all grids used were
unstructured, and the TGrid meshing scheme was used to generate unstructured tetrahedral
grids. Grids around the artificial reef were generated densely, and other domains were
generated sparsely to reduce unnecessary calculations.
Fig. 1. Computational grids
2.5 Finite volume discretization
The equations were solved using a FVM, where the equations were integrated over a control
volume. The control volume integrals were discretized into sums, which yielded discrete
equations. The discrete equations were applied to each control volume. The values of the
variables in the equations were solved by upwind discretization schemes. The basic concept
of upwind schemes is that the face value of a given variable is defined from the cell center
value in the cell upstream of the face. Upstream is defined relative to the fluid velocity
normal to the face. The second-order upwind schemes were employed for the turbulent
kinetic energy and turbulent energy dissipation rate here. In FLUENT6.3, all computational
work was performed with the 3D pressure-based solver in a first-order implicit unsteady
formulation. Gradients were estimated by the Green-Gauss cell-based method. The