A numerical scheme for morphological bed level calculations

Long, Wen; Kirby, James T.; Shao, Zhiyu

doi:10.1016/j.coastaleng.2007.09.009

Cited by 48 publications

(49 citation statements)

References 29 publications

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“…Saint-Cast (2002) applied the high-resolution NOC (Non-Oscillating Centered) scheme (based on Jiang and Tadmor, 1998) and bedform slope updating technique (suggested by Watanabe, 1988) to solve the sediment conservation equation without a filter or limiter. Shao et al (2004), Long et al (2008) and Chiang et al (2010) utilized the WENO (Weighted Essentially NonOscillatory) algorithm from the Computational Fluid Dynamics scheme (based on Liu et al, 1994 andJiang et al, 1999) to solve the 1D and 2D sediment conservation equation without any filters or limiters.…”

Section: Sample Computation and Discussionmentioning

confidence: 99%

“…The main concern of these studies is to stabilize the solutions when solving the sediment conservation equation. As reviewed in Long et al (2008), many state-of-the-art models introduce oscillation controlling schemes for bed form evolution modeling. The Delft Hydraulics model Delft2D-MOR (Roelvink et al 1994 and) utilizes a forward time, central space explicit scheme with a corrected sediment transport rate to offset the negative diffusion terms in the scheme.…”

Section: Sample Computation and Discussionmentioning

confidence: 99%

“…In order to control the oscillations in space for the morphological model, there are several numerical schemes as reviewed by Callaghan et al (2006) and Long et al (2008). Among these oscillation removal schemes, the NOC and WENO scheme are more stable finitedifference schemes than the others.…”

Section: Controlling Oscillations In Spatial Discretizationmentioning

confidence: 99%

“…Several numerical schemes are reviewed by Callaghan et al (2006), including a first order upwind scheme, two Lax-Wendroff schemes (Vincent andCaltagirone, 1999 andJohnson andZyserman, 2002) and the NOC scheme (Saint-Cast, 2002). Long et al (2008) review two Lax-Wendroff schemes (based on the Richtmyer scheme and the MacCormack scheme) and three WENO schemes (the TVD-RK-WENO scheme by Shao et al, 2004, the Euler-WENO scheme by Long et al, 2008 andBedlevel updated two-steps three-time-levels WENO scheme by Chiang et al, 2010). According to these reviewed results, Lax-Wendroff schemes or modified Lax-Wendroff schemes for morphodynamic system are not stable for long term simulation of bed level evolution.…”

Section: Modification Of Coastal Morphological Modelsmentioning

confidence: 99%

“…(13) and (14) should be updated in every time step after the new bed elevation is computed. Long et al (2008), Hsu and Hanes (2004), and Henderson et al (2004) address the appearance of wave phase-resolving sediment transport models for nearshore applications by waves and wave-driven nearshore currents. Because the wave orbital fluid motion is oscillatory in space and time, the resulting sediment transport fluxes should also be oscillatory.…”

Section: Analysis Of Oscillations For Morphological Schemementioning

confidence: 99%

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Coastal Morphological Modeling

Chiang¹,

Hsiao²

2011

Sediment Transport in Aquatic Environments

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The coastal zone is the area where the action of waves and wave-driven-currents on the seabed is very intense, and where the bed level and sediment are almost always in motion. If the mainly seasonal climate changes, the wind and wave conditions will also change. A new waves and wave-driven-currents conditions will change the rate of sediment transport and the beach topography. Natural beaches are significant characterized by an annual cycle of seasonal erosion and accretion. In other words, natural beaches are generally in dynamic equilibrium from the balance of sediment transport budge for specific area on the beach. We can utilize the conservation law of sediment transport to describe the coastal morphodynamic evolution. It is the same way to predict beach evolution due to changes in wave conditions or caused by coastal structures. Therefore, we can utilize numerical models to predict the change of bottom topography from the spatial distribution of the alongshore and offshore sediment transport rates in real coastal area. Coastal morphological models are indispensable and powerful tools that allow harbour and hydraulic engineers to predict nearshore topography, to analyze the impact of coastal structures, and to verify the planning and design of harbours and coastal defences. Morphological models are based on various sub-models for waves, tidal currents, nearshore currents, and sediment transport, coupled with the sediment transport model. The sediment transport model solves the sediment conservation equation to calculate bed-level evolution. The local sediment transport is first calculated by wave and current sub-models, and the bed form evolution is then computed based on the conservation of sediment and its continual redistribution in time. The aim of this chapter is to describe the theories, techniques, applications and robust algorithms for computing bed level change which is flexible enough to handle the nonlinearity present in the sediment conservation equations describing bed evolution in a complex coastal area. Classification of prediction methods for morphological evolutionThe changes of coastal topography were the complex and irreversible morphodynamic processes, influenced by local bathymetry, weather, wave, tide, and coastal structures, etc. The technology of prediction morphological evolution caused by coastal structures or varied with monsoon, typhoon, and climate changes, etc. is needed. In order to predict morphological evolutions, the experience analysis with many survey data in similar cases and the results of hydraulic model tests are considered in the past.

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Section: Sample Computation and Discussionmentioning

confidence: 99%

Section: Sample Computation and Discussionmentioning

confidence: 99%

Section: Controlling Oscillations In Spatial Discretizationmentioning

confidence: 99%

Section: Modification Of Coastal Morphological Modelsmentioning

confidence: 99%

Section: Analysis Of Oscillations For Morphological Schemementioning

confidence: 99%

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Coastal Morphological Modeling

Chiang¹,

Hsiao²

2011

Sediment Transport in Aquatic Environments

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A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

Benkhaldoun

Sahmim

Seaı̈d

2010

Numerical Methods in Fluids

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SUMMARYWe discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics.

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An efficient and flexible solver for the simulation of the morphodynamics of fast evolving flows on coarse sediment beaches

Briganti

Dodd

Kelly

et al. 2011

Numerical Methods in Fluids

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SUMMARY A well‐balanced total variation diminishing–McCormack scheme is used to simulate the fast evolving flow on a mobile coarse sediments bed. The scheme is chosen because of its shock capturing capabilities and its relative simplicity, which allow different sediment transport formulae to be slotted in easily. A typical example of the kind of flows treated here is bore‐driven wave run‐up. The analogy with a dam‐break on a mobile bed is used here to analyze the performance of the model. The model solves the nonlinear shallow water equations coupled with the Exner sediment balance equation for the mobile bed. Quasi‐analytical solutions to this problem for different expressions for instantaneous sediment discharge formulae are used to test the performance of the scheme. Together with the existing solution for the Grass formula, a further solution is obtained for a different formula. Numerical tests were also carried out for a further formula that is an industry standard. The agreement of the results with the solutions is very good and consistent results were obtained for all the formulae tested. Copyright © 2011 John Wiley & Sons, Ltd.

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A numerical scheme for morphological bed level calculations

Cited by 48 publications

References 29 publications

Coastal Morphological Modeling

Coastal Morphological Modeling

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

An efficient and flexible solver for the simulation of the morphodynamics of fast evolving flows on coarse sediment beaches

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