3 Dimensional Modeling of Advection-Diffusion Equation

Estimation of flows and sediment transport is challenging as many complexes and interacting physical phenomena need to be accounted for. In this research, a coupled two-dimensional finite volume flow model and a three-dimensional sediment transport model were developed in Fortran. In this model, the depth-integrated current vectors and water level were computed by 2D shallow water equations as the 2D model is computationally much faster than the 3D model. The depth-integrated current vectors were distributed in depths using a logarithmic current distribution equation, log of the wall. These distributed velocities and simulated water levels were used for three-dimensional sediment transport model which is generated using the same scheme. A 3D sediment transport model was preferred over a 2D model as 3D sediment model can estimate vertically diffusion of sediment mass from bedload to suspended sediment load which significantly improves the prediction of morphology evolutions.In order to discretize each subset of equations with the best-suited method, I utilized a time-splitting technique. As a result, I applied the second-order Fromm scheme which was found the best method for solving advection terms and semi-implicit forward time central space method which was found the best method for solving diffusion terms. The time-splitting scheme also reduced the complicity, therefore, the solution became simple and attractive to apply. For developing the sediment transport model, I applied this advection-diffusion concept to estimate the distribution of suspended sediment concentration and the Van Rijn (1981) scheme for the estimation of bedload sediment transport. As it’s very important to estimate and predict this phenomenon accurately, I compared the model with a lab trench experiment and the model results were in agreement with lab experiments. It was shown that the model could accurately simulate sedimentation on the downsloping (deceleration) section and erosion on the upsloping (acceleration) section of a marine trench. This would cause lateral movement of the channel toward the current direction. Being capable of accurate sediment transport and morphological dynamics simulation in this complex setting, this model is validated to be applied to other marine problems.