Accuracy of depth-integrated nonhydrostatic wave models

Depth-integrated nonhydrostatic models have been wildly used to simulate propagation of waves. Yet, there lacks a well-documented theoretical framework that can be used to assess the accuracy and scope of applications of these models and the related numerical approaches. In this work, we carry out Stokes-type Fourier and shoaling analyses to examine the linear and nonlinear properties of a popular one-layer depth-integrated nonhydrostatic model derived by Stelling and Zijlema (2003). The theoretical analysis shows that the model can satisfactorily interpret the dispersity for linear waves but presents evident divergence for nonlinear solutions even when kd → 0. A generalized depth-integrated nonhydrostatic formulation using arbitrary elevation as a variable is then derived and analyzed to examine the effects of neglecting advective and diffusive nonlinear terms in the previous studies and explore possible improvements in numerical solutions for wave propagation. Compared with the previous studies, the new generalized formulation exhibits similar dispersion relationship and improved shoaling effect. However, no significant improvement is presented for the nonlinear properties, indicating that retaining neglected nonlinear terms may not significantly improve the nonlinear performance of the nonhydrostatic model. Further analysis shows that the nonlinear properties of the depth-integrated nonhydrostatic formulation may be improved by defining variables at one-third of the still water level. However, such an improvement comes at the price of decreasing accuracy in describing dispersion and shoaling properties

A new multilayer nonhydrostatic formulation for surface water waves

This work presents a new multilayer nonhydrostatic formulation for surface water waves. The new governing equations define velocities and pressure at an arbitrary location of a vertical layer and only contain spatial derivatives of maximum second order. Stoke-type Fourier and shoaling analyses are carried out to scrutinize the mathematical properties of the new formulation, subsequently optimizing the representative interface and the location to define variables in each layer to improve model accuracy. Following the analysis, the one-layer model exhibits accurate linear and nonlinear characteristics up to kd = I, demonstrating similar solution accuracy to the existing second-order Boussinesq-type models. The two-layer model with optimized coefficients can maintain its linear and nonlinear accuracy up to kd = 4I, which boasts of better solution accuracy a larger application range than most existing fourth-order Boussinesq model and two-layer Boussinesq models. The three-layer model presents accurate linear and nonlinear characteristics up to kd = 10Ï, effectively removing any shallow water limitation. The current multilayer nonhydrostatic water wave model does not predefine the vertical flow structures, and more accurate vertical velocity distributions can be obtained by considering the velocity profiles in coefficient optimization

City-scale hydrodynamic modelling of urban flash floods: the issues of scale and resolution

Hydrodynamic models have been widely used in urban flood modelling. Due to the prohibitive computational cost, most of urban flood simulations have been currently carried out at low spatial resolution or in small localised domains, leading to unreliable predictions. With the recent advance in high-performance computing technologies, GPU-accelerated hydrodynamic models are now capable of performing high-resolution simulations at a city scale. This paper presents a multi-GPU hydrodynamic model applied to reproduce a flood event in a 267.4 km2 urbanised domain in Fuzhou, Fujian Province, China. At 2 m resolution, the simulation is completed in nearly real time, demonstrating the efficiency and robustness of the model for high-resolution flood modelling. The model is used to further investigate the effects of varying spatial resolution and using localised domains on the simulation results. It is recommended that urban flood simulations should be performed at resolutions higher than 5 m and localised simulations may introduce unacceptable numerical errors

Analytic study on long wave transformation over a seamount with a pit

In this paper, an analytic solution is derived for linear long waves scattering over a submarine seamount landform with a pit. The seamount is axisymmetric with a pit on the top. The water depth is defined by a trinomial function in the radial direction. The governing linear shallow water equation for long waves is expressed in the polar coordination, which is solved through separation of variables. As the topography is axisymmetric, solutions can be written as Fourier-cosine series. Waves over the seamount are expressed using Frobenius series expansion, while the water surface elevation in the outer region is expressed as Fourier-Bessel series, and the final solution is obtained by matching them at the conjunction. The solution can be degenerated into the previous analytic solutions for waves propagation over an axisymmetric pit or a submerged hump by adjusting the topography parameters

A novel two-way method for dynamically coupling a hydrodynamic model with a discrete element model (DEM)

The effect of floating objects has so far been little considered for hazard risk assessment and structure design, despite being an important factor causing structural damage in flood-prone and coastal areas. In this work, a novel two-way method is proposed to fully couple a shock-capturing hydrodynamic model with a discrete element model (DEM) for simulation of complex debris-enriched flow hydrodynamics. After being validated against an idealized analytical test, the new coupled model is used to reproduce flume experiments of floating debris driven by dam-break waves. The numerical results agree satisfactorily with the experimental measurements, demonstrating the model’s capability and efficiency in simulating complex fluid-debris interactions induced by violent shallow flows

A deterministic approach for assessing tsunami-induced building damage through quantification of hydrodynamic forces

In certain coastal areas across the globe, tsunamis pose a great threat to buildings, infrastructure and people's lives. The prevailing approaches for assessing building damage are based on probabilistic analysis. This paper introduces a new deterministic approach to assess large-scale building damage through quantifying lateral loading on structures induced by tsunami waves. A depth-averaged hydrodynamic model is adopted to simulate tsunami propagation and inundation and calculate the induced pressures and forces on structures. The model solves the 2D nonlinear shallow water equations (SWEs) using a finite volume shock-capturing numerical scheme and is implemented on Graphics Processing Units (GPUs) to achieve high-performance computing for large-scale applications. A new model component is included to calculate pressures and forces using the predicted flow variables, i.e. water depth and velocities. The resulting maximum tsunami forces are combined with a lateral force resisting system on each building to estimate damage states. This new approach is developed by taking advantages of a similar damage assessment method and the corresponding coefficients for quantifying earthquake impact on buildings, due to the similarity between the horizontal force systems induced by tsunami waves and earthquake motions. After being successfully validated against three experimental cases related to flow hydrodynamics, pressures and forces, the model is used to simulate a hypothetical 1000-year tsunami event in the City of Seaside, Oregon, USA. The resulting damage states are then classified for each of the urban buildings in the area, taking into account different building types. The predicted results are consistent with those obtained using alternative approaches, confirming the potential of the proposed approach for practical engineering applications

Hydrodynamic modelling of flow impact on structures under extreme flow conditions

Apart from the direct threat to human lives, the flood waves as a result of the rapid catchment response to intense rainfall, breaches of flood defences, tsunamis or storm surges may induce huge impact forces on structures, causing structural damage or even failures. Most existing design codes do not properly account for these impact forces due to the limited understanding of the underlying physical processes and the lack of reliable empirical formulae or numerical approaches to quantifying them. This paper presents laboratory experiments to better understand the interaction between the extreme flow hydrodynamics and the hydraulic structures and uses the measured data to validate a numerical model. The model solves the two-dimensional shallow water equations using a finite volume Godunov-type scheme for the reliable simulation of complex flow hydrodynamics. New model components are developed for estimating the hydrostatic and hydrodynamic pressure to quantify the flow impact on structures. The model is applied to reproduce two selected experiment tests with different settings and satisfactory numerical results are obtained, which confirms its predictive capability. The model will therefore provide a potential tool for wider and more flexible field-scale applications

Experimental and numerical investigation of fractal-tree-like heat exchanger manufactured by 3D printing

© 2018 Elsevier Ltd The manufacturing difficulties of complex fractal-tree-like heat exchangers have limited their industrial applications, although many evidences have shown that they have significant advantages in heat transfer. Nevertheless, the emerging 3D printing technology has brought great opportunity for the development of complex structured device. In the present study, three-dimensional (3D) fractal-tree-like heat exchangers were designed and manufactured using 3D printing technology. Their performance was evaluated from both thermal and hydrodynamic perspectives, the flow characteristics were investigated in detail. The results show that a fractal-tree-like heat exchanger can improve hydrodynamic performance, reduce pressure drops and has great heat transfer ability. In general, the fractal-tree-like heat exchanger has a comprehensive advantage over the traditional spiral-tube exchangers as it has a higher value of coefficient of performance (COP). Furthermore, the 3D printing provides a visual, efficient, and precise approach in the present research

Total Synthesis of (+)-SCH 351448: Efficiency via Chemoselectivity and Redox-Economy Powered by Metal Catalysis

The polyketide natural product (+)-SCH 351448, a macrodiolide ionophore bearing 14 stereogenic centers, is prepared in 14 steps (LLS). In eight prior syntheses, 22–32 steps were required. Multiple chemoselective and redox-economic functional group interconversions collectively contribute to a step-change in efficiency

Appendix S4. Ficus SSR data 11loci_278ind

Appendix S4. Ficus SSR data 11loci_278ind.tx