A 2D numerical model for simulation of cohesive sediment transport

Abstract

The study of the characteristics of fine-grained and cohesive sediments due to its filling characteristics in harbors and ports is an important subject in coastal studies. Fine-grained cohesive sediments have special complicated characteristics as compared to other sediments regarding their behavior. Hence, numerous research works have been carried out to establish well validated physical and mathematical descriptions of the behavior and outcome of concentrated near-bed cohesive sediment suspensions and their interaction with the water column and the bed as well as the turbulence characteristics of sediment laden flow. A two-dimensional model is developed in this study that includes: a cohesive sediment simulator module, processes such as advection and diffusion of cohesive sediment, flocculation and its effect on the settling velocity of cohesive sediment particles, consolidation of bed layers and sediment transport between layers, substrate shear stress variations affecting the simultaneous presence of wave and flow, bed morphology, deposition and erosion. In all these processes, the depth is considered according to the actual topography of the bed. For verification of model performance the model results have been compared with the MIKE 21 model results against the field data reported during the construction phase and at the simulation stage of Ho Bay, a case study presented by DHI (MIKE, 15). The comparisons indicate a favorable accuracy of the present model performance in simulation of cohesive sediment transport.

Appendix 1 The 2D hydrodynamic model

This paper utilizes the 2D hydrodynamic module of PMO-Dynamics, which was previously applied in the Caspian Sea modeling [2], for 2D hydrodynamic modeling. The model is applicable in different fields of coastal engineering, including simulations of tidal currents, wind-driven currents and Coriolis induced currents, currents in large scale environments (oceans), wave generated currents, large and small scale wave generation and wave propagation simulations, coastal morphology, sediment transportation and finally tidal analysis and tidal parameters extraction. The 2DH hydrodynamic module solves the Shallow Water Equations (SWE) which can be written in the conservative form as follow:

$$\frac{\partial \eta }{\partial t}+\frac{\partial p}{\partial x}+\frac{\partial q}{\partial y}=0$$

(A.1)

$$\frac{\partial p}{\partial t}+\frac{\partial }{\partial x}\left(\frac{{p}^{2}}{h}\right)+\frac{\partial }{\partial y}\left(\frac{pq}{h}\right)-{\Omega }q+gh\frac{\partial \eta }{\partial x}-{C}_{f}u\sqrt{{u}^{2}+{v}^{2}}-\frac{{\rho }_{a}}{{\rho }_{w}}{C}_{d}{u}_{w}\sqrt{{u}_{w}^{2}+{v}_{w}^{2}}=-\frac{h}{{\rho }_{w}}\frac{\partial {p}_{a}}{\partial x}+\frac{\partial }{\partial x}\left({\nu }_{t}\frac{\partial u}{\partial x}\right)+\frac{\partial }{\partial y}\left({\nu }_{t}\frac{\partial u}{\partial y}\right)$$

(A.2)

$$\frac{\partial q}{\partial t}+\frac{\partial }{\partial y}\left(\frac{{q}^{2}}{h}\right)+\frac{\partial }{\partial x}\left(\frac{pq}{h}\right)+{\Omega }p+gh\frac{\partial \eta }{\partial y}-{C}_{f}v\sqrt{{u}^{2}+{v}^{2}}-\frac{{\rho }_{a}}{{\rho }_{w}}{C}_{d}{v}_{w}\sqrt{{u}_{w}^{2}+{v}_{w}^{2}}=-\frac{h}{{\rho }_{w}}\frac{\partial {p}_{a}}{\partial y}+\frac{\partial }{\partial x}\left({\nu }_{t}\frac{\partial v}{\partial x}\right)+\frac{\partial }{\partial y}\left({\nu }_{t}\frac{\partial v}{\partial y}\right)$$

(A.3)

where $t$ is the time, $x$ and $y$ are Cartesian coordinates, $g$ is gravitational acceleration, $\eta$ is water surface elevation, $u$ and $v$ are velocity components, $h$ is water depth, $p=uh$and $p=vh$ are flux components, ${u}_{w},{v}_{w}$= are wind velocity components, ${C}_{d}$ is air-fluid drag coefficient, ${C}_{f}$ is friction coefficient, ${p}_{a}$is air pressure, ${\nu }_{t}$is eddy viscosity and ${\Omega }$ is Coriolis parameter.

This model solves the equation on mesh vertex layout. More details and verifications for this model were presented by Namin et al. [16]. The second-order Roe scheme on an unstructured grid has been used to solve SWE. Figure 13 shows the outline of the numerical procedure used to solve the advection-diffusion equation.

Fig. 13

The outline of the numerical procedure used to solve the advection-diffusion equation