Ahmad, Nadeem (Norwegian University of Science and Technology (NTNU)) | Bihs, Hans (Norwegian University of Science and Technology (NTNU)) | Chella, Mayilvahanan Alagan (Norwegian University of Science and Technology (NTNU)) | Kamath, Arun (Norwegian University of Science and Technology (NTNU)) | Arntsen, Øivind A. (Norwegian University of Science and Technology (NTNU))
Computational fluid dynamics (CFD) modeling of breaking waves over a slope and the resulting erosion in the case of an Arctic coastline is presented in this study. The study is performed with the open-source numerical model REEF3D. First, the numerical model is validated for the simulation of incident waves, wave breaking on a slope, and the sediment transport process. The numerical results show good agreement with wave theory and experimental data. The validated numerical model for the hydrodynamics and the sediment transport process is then used to simulate the coastal erosion process under the breaking wave impact on a vertical bluff. An Arctic coastline at Bjørndalen region at Isfjorden, Svalbard, is chosen, where a significant coastal erosion was observed during a storm event in September 2015.
Most of the Arctic coastline is susceptible to climate change. Because of global warming and the transfer of additional heat fluxes, the frozen period of the upper active layers in the Arctic coastline is reduced. Consequently, coastline stability decreases during the extended warmer period. The average thickness of the active sediment layer in Svalbard, Norway, varies between 1.0 and 10.0 m and consists of coarse-grained sandy soil (Fromreide, 2014). Climate change can affect this Arctic coastline in two ways. First, the extended warmer period results in the formation of deeper and weaker active sediment layers (IPCC, 2007). Second, the melting of the Arctic ice sheets increases the sea level, resulting in higher tides. In combination, the higher tides approach the Arctic coastline (Thompson et al., 2016) and erode the weaker active sediment layer. A recent example of this change has been experienced in the Bjørndalen region in Isfjorden, Svalbard, where significant coastal erosion occurred during a storm event in September 2015. The waves reached the cabins built near Isfjorden and resulted in an almost 1.0-m-deep scour hole (Barstein, 2015). Therefore, in order to better understand the coastal erosion phenomenon in the Arctic regions, the processes of wave breaking and the resulting sediment transport have to be investigated in detail. The study is also important for the design of new coastal structures and suitable mitigation measures at the Arctic coastline.
In the current paper, a novel three dimensional numerical wave tank is presented. The numerical model uses the level set method for the prediction of the interface between the two phases water and air. The free surface is modeled as the zero level set of a scalar signed distance function. In order to maintain this property and to ensure mass conservation, the level set function is reinitialized after each time step. The conservative fifth-order finite difference WENO scheme is used for the discretization of the convective terms. For large gradients and even shocks the scheme ensures a smooth and oscillation free solution, while at the same time maintaining a high order of accuracy. With this scheme the wave damping due to numerical diffusion is kept at a minimum. The pressure is treated with the projection method on a staggered grid, which prevents velocity-pressure decoupling. A preconditioned BiCGStab algorithm is employed for the iterative solution of the Poisson equation. For discretization in time a third-order TVD Runge-Kutta scheme is used. Parallelization of the numerical model is achieved by using the domain decomposition framework together with the MPI library. Since the numerical model employs a Cartesian grid, the present study requires special attention to complex geometries. Here an immersed boundary method based on ghost cell extrapolation is used. As the numerical model is used as a numerical wave tank, wave generation is required for the inlet boundary. Wave generation is modeled through a transient velocity and water elevation profile obtained from wave theory and is implemented through a relaxation zone. Wave reflections of the downstream boundary are prevented by the implementation of a numerical beach.
The numerical wave tank is validated through comparison between numerical and theoretical wave profiles in a two-dimensional wave flume setup. Here the advantage of the level set solver with its high order of accuracy is highlighted, exhibiting negligible wave damping due to numerical diffusion. The three dimensional capabilities of the numerical wave tank are shown for the calculation of waves and runup over a circular island. The results show good agreement with experimental data, the detailed free surface can be reproduced by the numerical model.
Before the deployment of Oscillating Water Column (OWC) devices for commercial ocean energy harvesting, comprehensive studies on the hydrodynamics of the device are essential. CFD modelling allows for a thorough testing of the influence of various parameters on the performance of an OWC device. In the current paper, a two-dimensional numerical wave tank is used to study the interaction of linear waves with an OWC wave energy converter device. Numerical experiments over a range of wave lengths for a certain front wall draught and thickness with different nozzle widths are carried out. Theory of porous media flow is used in addition to the nozzle to simulate external damping. The movement of the free surface inside the device is calculated in two-dimensions to obtain a realistic visualisation of the hydrodynamics inside the device. The hydrodynamic efficiency of the device is used to measure the performance of the device. The impermeability factor used at the nozzle using porous media flow provides results that closely follow the experimental results. The numerical model uses a uniform cartesian staggered computational grid with velocities at the cell edges and pressure at the cell centres. Fluid flow is governed by the Reynolds-Averaged Navier-Stokes equations. A 5th-order conservative finite difference WENO scheme is employed for the discretization of the convective terms. Time discretization is carried out using the 3rd-order TVD Range-Kutta scheme. The projection method is used for pressure discretization and the Poisson equation for pressure is solved using a preconditioned BiCGStab solver. Wave generation and dissipation in the wave tank is carried out by the relaxation method. The level set method, which uses a function that is smooth over the interface, is used to determine the free surface. This provides a sharp interface between water and air in the wave tank enabling the detail in the simulations. The computing performance of the code is increased by parallel processing using the OpenMPI library.