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The numerical modeling of sediment transport under wave impact is challenging because of the complex nature of the triple wave–structure–sediment interaction. This study presents three-dimensional numerical modeling of sediment scouring due to non-breaking wave impact on a vertical seawall. The Navier–Stokes–Exner equations are approximated to calculate the full evolution of flow fields and morphodynamic responses. The bed erosion model is based on the van Rijn formulation with a mass-conservative sand-slide algorithm. The numerical solution is obtained by using a projection method and a fully implicit second-order unstructured finite-volume method in a σ-coordinate computational domain. This coordinate system is employed to accurately represent the free-surface elevation and sediment/water interface evolution. Experimental results of the velocity field, surface wave motion, and scour hole formation hole are used to compare and demonstrate the proposed numerical method’s capabilities to model the seawall scour.
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A full 3D numerical model is used for studying tidal asymmetry, estuarine circulation, and saline intrusion in the Gironde estuary. The model is calibrated and verified using the data measured during two field surveys in the Gironde estuary. Harmonic analysis of numerical results is proposed to understand how the superposition of M2, M4 and M6 components generate a complex estuarine circulation and salinity intrusion in the Gironde estuary. The numerical results show that the M6 component plays a significant role as important as the M4 one in modifying the nature of tidal asymmetry, especially in the Gironde upper estuary. In this case, the use of the phase lag between M2 and M4, neglecting M6, to predict the tidal asymmetry nature could produce errors. The effect of asymmetrical tides on saline intrusion and residual circulation is specifically discussed here.
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Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.
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A three-dimensional large eddy simulation model is used to simulate the turbulent flow dynamics around a circular pier in live-bed and clear-water scour conditions. The Navier–Stokes equations are transformed into a σ-coordinate system and solved using a second-order unstructured triangular finite-volume method. We simulate the bed evolution by solving the Exner-Polya equation assisted by a sand-slide model as a correction method. The bedload transport rate is based on the model of Engelund and Fredsœ. The model was validated for live-bed conditions in a wide channel and clear-water conditions in a narrow channel against the experimental data found in the literature. The in-house model NSMP3D can successfully produce both the live-bed and clear-water scouring throughout a stable long-term simulation. The flow model was used to study the effects of the blockage ratio in the flow near the pier in clear-water conditions, particularly the contraction effect at the zone where the scour hole starts to form. The scour depth in the clear water simulations is generally deeper than the live-bed simulations. In clear-water, the results show that the present model is able to qualitatively and quantitatively capture the hydrodynamic and morphodynamic processes near the bed. In comparison to the wide channel situation, the simulations indicate that the scour rate is faster in the narrow channel case.
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Every year, in the Vietnam Mekong Delta Coastal Zone (VMDCZ), erosions cause approximately 300 ha of agricultural land loss. Therefore, measures for shoreline protection are urgently needed. This paper discusses the impacts of protection measures in the Go-Cong Coastal Zone to prevent erosion/accretion processes, predicted by two numerical models, MIKE21-FM and TELEMAC-2D. Hard and soft measures have been proposed using breakwaters and sandbars, respectively. The simulations show that the erosion/accretion trends provided by both models are similar. For breakwaters, MIKE21-FM provides less accretion than TELEMAC-2D in areas extending over 300 m and 500 m from shorelines. However, for sandbars, MIKE21-FM shows higher accretion within areas extending over 500 m but less than 300 m. Sandbars cause higher accretion in a larger area, extending over 1000 m offshore. The simulation results allow us to propose two alternative measures: (1) a row of several breakwater units will be implanted at 300 m offshore. The length of each unit is 600 m, with a gap between two neighbouring units of 70 m and a crest elevation of 2.2 m above mean sea level (MSL). (2) A row of sandbar units will be posed at 500 m offshore, with a unit length of 1000 m and a gap between the two neighbouring units of 200 m. The crest elevation is fixed at MSL.
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This paper presents experimental and numerical studies on the erosion of a horizontal granular bed by a two-dimensional plane vertical impinging jet to predict the eroded craters’ size scaling (depth and width). The simulations help understand the microscopic processes that govern erosion in this complex flow. A modified jet-bed distance, accounting for the plane jet virtual origin, is successfully used to obtain a unique relationship between the crater size and a local Shields parameter. This work develops a two-phase flow numerical model to reproduce the experimental results. The numerical techniques are based on a finite volume formulation to approximate spatial derivatives, a projection technique to calculate the pressure and velocity for each phase, and a staggered grid to avoid spurious oscillations. Different options for the sediment’s solid-to-liquid transition during erosion are proposed, tested, and discussed. One model is based on unified equations of continuum mechanics, others on modified closure equations for viscosity or momentum transfer. A good agreement between the numerical solutions and the experimental measurements is obtained.