Juntao Zhou

The Severn Estuary has the world’s second largest tide range and a barrage across the estuary, located just seawards of Cardiff in Wales and Weston in the South West England, has been proposed for over half a century, with the objective of extracting large amounts of tidal energy. A Severn Barrage, as previously proposed by the Severn Tidal Power Group (STPG), would be the largest renewable energy project for tidal power generation in the world, if built as proposed, and would generate approximately 5% of the UK's electricity needs. However, concerns have been raised over the environmental impacts of such a barrage, including potential increase in flood risk, loss of intertidal habitats etc. In addressing the challenges of maximising the energy output and minimising the environmental impacts of such a barrage, this research study has focused on using a Continental Shelf model, based on the modified Environmental Fluid Dynamics Code (EFDC) with a barrage operation module (EFDC_B), to investigate both the far and near field hydrodynamic impacts of a barrage for different operating scenarios. Three scenarios have been considered to simulate the Severn Barrage, operating via two-way generation and using different combinations of turbines and sluices. The first scenario consisted of 216 turbines and 166 sluices installed along the barrage; the second consisted of 382 turbines with no sluices; and the third consisted of 764 turbines and no sluices. The specification of the sluice gates and turbines are the same for all scenarios.  The model results indicate that the third scenario has the best mitigating effects for the far-field and near-field flood risks caused by a barrage and produces the most similar results of minimum water depth and maximum velocity distributions to those obtained from simulating the natural conditions of the estuary, i.e. the current conditions. The results also show that the flow patterns around the barrage are closest to those for the existing natural conditions with minimal slight changes in the estuary. Thus, the results clearly indicate that the environmental impacts of a Severn Barrage can be minimised if the barrage is operated for two-way generation and under the third scenario. Although it appears that the energy output for the third scenario is less than that obtained for the other two scenarios, if very low head (VLH) turbines are used, then the third scenario could generate more energy as more turbines could be cited along the barrage structure. Therefore, the study shows that a Severn Barrage, operating in two-way generation and with 764 turbines (ideally VLH turbines), would be the best option to meet the needs of maximising the energy output, but having a minimal impact on environmental changes in the estuary and far-field.

The Severn Estuary has the second largest tide range in the world and a barrage across the estuary from Cardiff in South Wales to Weston in South West England has been proposed for over half a century, to extract large amounts of tidal energy from the estuary. To assess the environmental impacts of the proposed tidal barrage requires accurate model predictions of both the near-field and far-field hydrodynamics, which can strongly depend on the model area and the appropriate boundary forcing. In this paper two models, based on the Environmental Fluid Dynamics Code (EFDC) numerical model with a recently-developed Barrage module (EFDC_B), were set up with different computational domains. The Continental Shelf model, which was centred on the Bristol Channel, has its open boundary extended to beyond the Continental Shelf. The Irish Sea model, which was also centred around the Bristol Channel, only has its open boundary extended to the Celtic Sea in the south and the Irish Sea in the north. In order to investigate the effects of the open boundary conditions imposed in the models on the near and far-field hydrodynamics for the case of the Severn Barrage, the Continental Shelf model was first run with and without the operation of the Severn Barrage. The Irish Sea model was then run, also with and without the operation of the Severn Barrage, and with the open boundary conditions provided by the Continental Shelf model. The results from both models were then analysed to study the impact of the tidal barrage on the near-field and far-field hydrodynamics in the Bristol Channel and Irish Sea. Detailed comparisons of the model results indicate that the hydrodynamic conditions along the open boundaries of the Irish Sea model are affected by the tidal barrage and that the open boundary conditions also have noticeable impacts on the far-field hydrodynamics, especially in the Irish Sea, with approximately an average 4-7 cm difference in the maximum water levels predicted in Cardigan Bay and with a maximum difference of 9 cm in the northern part of Cardigan Bay.

This paper presents an investigation of the impacts of a Severn Barrage on the hydro-environment of the Bristol Channel and Severn Estuary using the Environmental Fluid Dynamics Code (EFDC) model with a recently developed Barrage module (EFDC_B). Details are given of a barrage module being implemented into the EFDC model to represent the various hydraulic structures, such as turbines and sluice gates, as deployed along the barrage line. Several cases, both with and without the barrage, have been simulated to investigate the potential changes on the peak water levels, minimum water depths and peak tidal currents arising from a barrage. The impacts of a barrage on the salinity concentration distribution have also been simulated in both 2D and 3D modes. The predicted results showed that the maximum water levels could be significantly reduced, especially downstream of the barrage and for much of the region in the Severn Estuary and that the minimum water depths would be changed so much that there would be 80.5 km2 loss of intertidal habitats due to the sitting of a barrage across the estuary. Likewise, the peak tidal currents would be considerably reduced, and by as much as a half in the middle of the main channel. The predicted salinity concentrations results indicated that at high water, the salinity concentrations would be reduced by 1–2 ppt downstream and upstream of the barrage and salinity concentrations in the region near Beachley would be reduced by up to 5 ppt, and that at low water, salinity concentrations would be reduced by 0.5–1 ppt in the middle of the Bristol Channel and by typically 0.5 ppt and 1 ppt downstream and upstream of the barrage, respectively. The predicted results also indicated that salinity concentrations downstream and upstream of the barrage would be under a stable state with slight oscillations all the time due to the effects of the barrage. A comparison between the salinity concentration distributions predicted by the 2D and 3D models indicated that the two models produced similar salinity distributions, especially in the Severn Estuary and in the region between the middle of the Bristol Channel and the seaward open boundary.

An alternating direction explicit (ADE) scheme to solve the unsteady convection–diffusion equation with Robin boundary conditions is presented and discussed in this paper. It was derived based on the local series expansion method and proved unconditionally stable by von Neumann stability analysis. Thereafter, the ADE scheme is compared with the conventional schemes, and a comparison between the amplification factor of all schemes and the exact one shows that the proposed scheme can simulate well both convection- and diffusion-dominated problems. Finally, the proposed method was validated by a numerical experiment which indicates that, for large cell Reynolds numbers, the proposed scheme, which has unconditional stability, is more accurate than implicit schemes and most explicit schemes. It is also shown that the proposed scheme is simple to implement, economical to use, effective for dealing with Robin boundary conditions and easy to apply to multidimensional problems.

In practical engineering applications, convection diffusion equations are generally used to describe the transport processes involving fluid motion, heat transfer, astrophysics, oceanography, meteorology, semiconductors, hydraulics, pollutant & sediment transport and chemical engineering. In this paper, a high order compact difference scheme based on the fourth order compact difference scheme in spatial discretization and the fourth order Runge-Kutta method in time integration is proposed for the numerical simulation of the unsteady convection-diffusion equation. The validity and effectiveness of the proposed method is firstly tested by a two-dimensional convection-diffusion equation with a Gaussian pulse type concentration. The L 2 error norms are used to measure differences between the exact and numerical solutions and compared to those obtained by other methods. It is shown that the results obtained by proposed method agree very well with the analytical solutions and is more accurate than other methods. Then, a two-dimensional non-linear Burgers equation is used to validate the effectiveness of the proposed method used to solve the non-linear convection-diffusion equation, which also models well. Finally, the Taylor’s vortex problem is investigated by the proposed method and good agreement is obtained with the exact solutions. From the three test problems, it is shown that the proposed high order compact difference scheme is an efficient and accurate method to simulate the transport problems and also can be applied to many engineering problems.

A numerical simulation of the regularized long wave (RLW) equation is obtained using a high-order compact difference method, based on the fourth-order compact difference scheme in space and the fourth-order Runge–Kutta method in time integration. The method is tested on the problems of propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves, the development of an undular bore and the solitary waves induced by boundary motion. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. L2 and L∞ error norms are used to measure differences between the exact and numerical solutions. The results obtained by proposed method are compared with those of other recently published methods and shown to be more accurate and efficient. Copyright © 2006 John Wiley & Sons, Ltd.

Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage, a cubic spline function is adopted at correcting stage, which made the time discretization accuracy up to fourth order; For spatial discretization, a three-point explicit compact difference scheme with arbitrary order accuracy is employed. The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme. The numerical results agree well with the experimental data. At the same time, the comparisons of the two numerical results between the present scheme and low accuracy difference method are made, which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations. As a valid sample, the wave propagation on the rectangular step is formulated by the present scheme, the modelled results are in better agreement with the experimental data than those of Kittitanasuan.

Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysis. Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convection-diffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.

It will take long computational time for Monte-Carlo Method (MCM) to deal with the potential flow, which has big scale and more grid. The drawback of the problem becomes more apparent especially when the number of random walk is added. According to the problem, in this paper, a quick calculation method based on MCM is presented. In this method, a transfer probability based on angle is proposed. And the random walk model and examples are given accordingly. With the same number of random walk, the comparison with results shows that the improved method in this paper costs much less time than common MCM. The method presented in this paper not only shortens the calculation time, but also extends the application of MCM.