Existing numerical river models are mostly built upon asynchronous solution of simplified governing equations. The strong coupling between water flow, sediment transport, and morphological evolution is thus ignored to a certain extent. An earlier study led to the development of a fully coupled model and identified the impacts of simplifications in the water-sediment mixture and global bed material continuity equations as well as of the asynchronous solution procedure for aggradation processes. This paper presents the results of an extended study along this line, highlighting the impacts on both aggradation and degradation processes. Simplifications in the continuity equations for the water-sediment mixture and bed material are found to have negligible effects on degradation. This is, however, in contrast to aggradation processes, in which the errors purely due to simplified continuity equations can be significant transiently. The asynchronous solution procedure is found to entail appreciable inaccuracy for both aggradation and degradation processes. Further, the asynchronous solution procedure can render the physical problem mathematically ill posed by invoking an extra upstream boundary condition in the supercritical flow regime. Finally, the impacts of simplified continuity equations and an asynchronous solution procedure are shown to be comparable with those of largely tuned friction factors, indicating their significance in calibrating numerical river models. It is concluded that the coupled system of complete governing equations needs to be synchronously solved for refined modeling of alluvial rivers.

Coupled and Decoupled Numerical Modeling of Flow and Morphological Evolution in Alluvial Rivers

Non-uniform adaptive vertical grids for 3D numerical ocean models

Drying wetting approach for 3D finite element sigma coordinate model for estuaries with large tidal flats

Three dimensional numerical modelling of wind driven circulation in a homogeneous lake

A three-dimensional, non-hydrostatic pressure, numerical model with k-e equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non-hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non-hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure-Poisson equation is solved iteratively with a preconditioned linear GMRES method

A 3-D non-hydrostatic pressure model for small amplitude free surface flows

A new efficient numerical method for three-dimensional hydrodynamic computations is presented and discussed in this paper. The method is based on the operator splitting method and combined with Eulerian–Lagrangian method, finite element method and finite difference method. To increase the efficiency and stability of the numerical solutions, the operator splitting method is employed to partition the momentum equations into three parts, according to physical phenomena. A time step is divided into three time substeps. In the first substep, advection and Coriolis force are solved using the explicit Eulerian–Lagrangian method. In the second substep, horizontal diffusion is approximated by implicit FEM in each horizontal layer. In the last substep, the continuity equation is solved by implicit FEM, and vertical diffusion and pressure gradient are discretized by implicit FDM in each nodal column. The stability analysis shows that this method is unconditionally stable. A number of numerical experiments have been performed. The results simulated by the present scheme agree well with analytical solutions and the other documented model results. The method is efficient for 3D shallow water flow computations and fully fits complicated configurations. © 1998 John Wiley & Sons, Ltd.

An efficient operator splitting scheme for three‐dimensional hydrodynamic computations

A multi-layer water-sediment predictive model has been developed to study the effects of coastline reconfigurations on the three-dimensional (3-D) flow and sediment fields in coastal waters. The model is gridded with finite elements in the horizontal domain for easy adaptation to complex boundary configurations. The non-uniformity of flow and sediment distributions in the water column are represented by multiple vertically averaged layers. The Lax-Wendroff two-step scheme is used for time marching. This allows the flow field and sediment field to be explicitly coupled so that the density of the water-sediment mixture and the flow depth are updated without matrix inversion for the advanced time level. Because of the adoption of the explicit time-marching scheme, the allowed time increment of the present numerical scheme is relatively small. However, this is beneficial to studying short life activities such as sediment entrainment and deposition. The model predicted results were tested against field measure...

Multi-layer modeling of three-dimensional hydrodynamic transport processes

The accuracy of three-dimensional (3D) mass transport modeling strongly relies on how well the vertical structures of the transport processes are resolved with the model resolution. The widely used vertical “stair-stepped” and topography following sigma (σ)-coordinate systems are fixed in time and space. Hence, these techniques often fail to resolve the details of the time varying, and highly nonlinear, activities in the water column. To better capture the geometrical details of these activities, a new vertical solution-adaptive grid method is introduced in this paper. The method takes into account the gradient variation of a selected variable in the mass transport field as an additional controlling factor in σ-coordinate transformation and so the new transformed grid is called a \hGradient-\hAdaptive-\hSigma (GAS) grid. The transformed grid spacing automatically adjusts in time and space according to the local solution gradient of the selected variable and converges in the high gradient regions for better resolution. The solution-adaptive method is implemented in a surface water numerical model to transform Cartesian coordinates into GAS coordinates. The model is established on the basis of an operator splitting scheme coupled with a Eulerian-Lagrangian method. Four numerical experiments describing the sediment transport activities of net entrainment and net deposition, and also pollutant dispersion, are performed with the transformed model. The computed results agree with the laboratory measurements. A comparison between the results computed by the GAS-gridded model and a σ-gridded model shows that using the GAS-grid arrangement can improve the solution accuracy by as much as one-fold in regions of high solution gradients.

Gradient-Adaptive-Sigma (GAS) Grid for 3D Mass-Transport Modeling

This paper describes the formulation and verification of a newly developed three dimensional sediment transport model for coastal waters. The multi-layer finite element method (Kawahara et al., 1978 and Li and Zhan, 1993) has been adopted to improve the ability for model boundary adaptation with actual coastal geometry which is essential for accurate sediment transport simulations. The incorporation of laboratory determined sediment parametric functions in the model to resolve the sediment transport mechanisms such as the bed deformation, sediment entrainment and deposition, and stratification is also emphasized. The model was applied to compute the suspended sediment conditions for an idealized case as well as a practical application in Hong Kong waters. The strong correlation revealed in the comparisons between the computed and observed results indicates that the present model can serve as an effective tool for sediment transport studies on harbor and port development and management.

A Multi-Layer Finite Element Formulation for Suspended Sediment Transport in Tidal Flows

Data collection and modeling in support of the mid-breton sediment diversion project

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