SRH-2D numerical model
The Sedimentation and River Hydraulics-Two-Dimensional model (SRH-2D)
was implemented in this study. The SRH-2D is a module integrated into
the surface water modeling system package (SMS-2D) which is a
comprehensive package of tools for simplifying the development of 2D
hydraulic models. (SRH-2D) is a 2D hydraulic numerical model based on 2D
hydraulic principles for river hydraulics and sediment transport
developed at the U.S. Bureau of Reclamation (USBR) (Aquaveo 2013).
(SRH-2D) solves the time and depth-averaged Navier Stokes equations
(known as the depth-averaged St.Venant Equations) to govern the flow
regime (Lai and Greimann 2008) as follows:
\(\frac{\mathbf{\partial H}}{\mathbf{\partial t}}+\frac{\mathbf{\partial HU}\ }{\mathbf{\partial x}}+\frac{\mathbf{\partial hV}\text{\ \ }}{\mathbf{\partial y}}=0\)(1)
\(\frac{\mathbf{\partial HU}\text{\ \ }}{\mathbf{\partial t}}+\frac{\mathbf{\partial HUU}\ }{\mathbf{\partial x}}+\frac{\mathbf{\partial HVU}\text{\ \ \ }}{\mathbf{\partial y}}=\frac{\mathbf{\partial H}\mathbf{T}_{\mathbf{\text{xx}}}}{\mathbf{\partial x}}+\ \frac{\mathbf{\partial H}\mathbf{T}_{\mathbf{\text{xy}}}}{\mathbf{\partial y}}-\text{gH}\ \frac{\mathbf{\partial z}}{\mathbf{\partial x}}-\frac{\mathbf{\tau}_{\mathbf{\text{bx}}}}{\mathbf{\rho}}\)(2)
\(\frac{\mathbf{\partial HV}}{\mathbf{\partial t}}+\frac{\ \mathbf{\partial HUV}}{\mathbf{\partial x}}+\frac{\mathbf{\partial HVV}}{\mathbf{\partial y}}=\frac{\mathbf{\partial H}\mathbf{T}_{\mathbf{\text{xy}}}}{\mathbf{\partial x}}+\frac{\mathbf{\partial H}\mathbf{T}_{\mathbf{\text{yy}}}}{\mathbf{\partial y}}-\text{gH}\frac{\mathbf{\partial z}}{\mathbf{\partial y}}-\frac{\mathbf{\tau}_{\mathbf{\text{by}}}}{\mathbf{\rho}}\)(3)
where x and y: horizontal cartesian coordinates, t: time, H: water
depth, U, V: depth-averaged velocity in x and y directions respectively,
g: gravitational acceleration, T𝑥𝑥, T𝑥𝑦,
T𝑦𝑦: depth-averaged stresses due to turbulence,
𝜏𝑏𝑥, 𝜏𝑏𝑦: bed shear stresses, 𝜌: water
density, Z=Z𝑏 + h, Z: water surface elevation,
Z𝑏: bed elevation.
Mesh generation and boundary
conditions
The generated mesh which represents the study area using the SRH-2D
numerical model consists of a total number of 180,000 triangular
elements with a minimum width of 30m. The bed level elevation was
assigned to mesh elements at each node. The upstream boundary conditions
are the flow discharge from the delta barrage and five drains. The
downstream boundary condition is the water level at the Shabrakhet gauge
station corresponding to the upstream flow as shown in Figure 3.
Model calibration and
verification
The numerical model was calibrated using flow discharge of the year 2021
with the corresponding water level and stream velocity at two
cross-sections as shown in Figure 4. The best suitable value for the
manning roughness coefficient (n) is 0.015 after several model
simulations. The numerical model was also verified using flow discharge
of the year 2018 with the corresponding water level and stream velocity
at two cross-sections as shown in Table 1. Model performance was
verified by