Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling

In this paper an efficient numerical method based on hybrid finite element and finite volume techniques to solve hurricane induced storm surge flow problem is presented. A segregated implicit projection method is used to solve the 2D shallow water equations on staggered unstructured meshes. The governing equations are written in non-conservation form. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered finite volume method. The nonlinear wave equation is solved by the node-based Galerkin finite element method. This staggered-mesh scheme is distinct from other conventional approaches in that the velocity components and auxiliary variables are stored at cell centers and vertices, respectively. The present model uses an implicit method, which is very efficient and can use a large time step without losing accuracy and stability.The hurricane induced wind stress and pressure, bottom friction, Coriolis effect, and tidal forcing conditions are implemented in this model. The levee overtopping option is implemented in the model as well. Hurricane Katrina (2005) storm surge has been simulated to demonstrate the robustness and applicability of the model.     

Effects of submersion depth on wave uplift force acting on Biloxi Bay Bridge decks during Hurricane Katrina

A large portion of the Biloxi Bay Bridge was submerged and destroyed by surface waves and storm surge associated with Hurricane Katrina in 2005. In this paper, the time history of wave forces exerted on the Biloxi Bay Bridge during Hurricane Katrina was investigated by a wave-loading model. The Volume of Fluid (VOF) method was adopted in the model to track the variations of water surface levels. In order to obtain wave parameters and storm-surge elevation at the bridge site during Hurricane Katrina, a storm surge model and a wave propagation model were coupled to hindcast the hydrodynamic conditions. Outputs of the coupled wave-surge models were imported to the wave-loading model to simulate the dynamic wave forces acting on the bridge deck. In order to evaluate the maximum uplift wave force, five different bridge deck elevations submerged at different water depths were investigated. The processes of wave-bridge interaction were simulated by the wave-loading model. The wave profiles, velocity field in the vicinity of the bridge, and dynamic wave forces on the decks were analyzed. Results indicate that the uplift force on the submerged bridge deck span exceeded its own weight under the extreme wave and storm surge conditions during Hurricane Katrina. Moreover, the numerical simulations suggest that the maximum uplift wave force occurred when the storm surge water level reached the top of the bridge deck.     

Modelling coastal barrier breaching flows with well-balanced shock-capturing technique

This paper presents a coastal hydrodynamic model for simulating coastal barrier breaching flows through an inlet which are mostly induced by extreme hydrological conditions such as storm/hurricane surges, waves and tides. In order to simulate wave field and wave-induced flow field in a coast, a wave action spectral model is coupled with a hydrodynamic model. The Godunov-type shock-capturing technique is used in the hydrodynamic model to simulate the supercritical flows and shocks driven by the extreme storm conditions. The hydrodynamic model is based on the solution of depth-averaged non-linear shallow water equations with all physical forcings common to coastal hydrological conditions so that it is capable of simulating multiple flow regimes, in which subcritical, transcritical, or supercritical flows may happen. The bed slope terms in the system of equations are treated in such a way that exact balance between flux gradient and bed slope terms is achieved under still water condition. The wave model readily provides the radiation stresses that represent the shortwave-averaged forcings in a water column and take into account wave-induced nearshore currents. In the coupled system, the models are operated systematically. The coastal hydrodynamic model is shown to accurately reproduce analytical and benchmark numerical solutions. To further test the accuracy of the model, flow through a coastal inlet with a storm surge is simulated and the results are compared with an established coastal flow model. Finally, the model is examined to simulate a severe storm surge that develops supercritical flows and the results are found to be encouraging.     

A multiple-layer σ-coordinate model for simulation of wave-structure interaction

A 3D multiple-layer σ-coordinate model has been developed to simulate surface wave interaction with various types of structures including submerged structures, immersed structures, and floating structures. This model is the extension of the earlier model [Lin P, Li CW. A σ-coordinate three-dimensional numerical model for surface wave propagation. Int J Numer Methods Fluid 2002;38(11):1045-68] that solves Navier-Stokes equations in the transformed σ-coordinate, which is especially efficient for simulation of wave propagation over varying topography. By introducing the layered σ-coordinates, the present model overcomes the difficulty encountered by the earlier model in calculating waves past a depth discontinuity, e.g., a submerged rectangular breakwater. Furthermore, with the employment of 3-layer σ-coordinate the present model is able to simulate flow interaction with an immersed body or a floating body. The new model is validated against an established Volume-Of-Fluid (VOF) model [Lin P, Liu PL-F. A numerical study of breaking waves in the surf zone. J Fluid Mech 1998;359:239-64] for the 2D solitary wave interaction with a submerged, immersed, or floating rectangular obstacle. For the solitary wave interaction with a submerged breakwater, the numerical results are also compared to the experimental data by Zhuang and Lee [A viscous rotational model for wave overtopping over marine structure. In Proc 25th Int Conf Coast Eng, ASCE, 1996. p. 2178-91] and very good agreements have been obtained for velocities in the vortex behind the structure. Finally, the present model is used to simulate 3D wave interaction with a Very Large Floating Structure (VLFS) above a submerged shoal. It is proved that the model is an accurate and efficient numerical tool to investigate different wave-structure interactions problems.     

Performance of the Unstructured-Mesh, SWAN+ADCIRC Model in Computing Hurricane Waves and Surge

Coupling wave and circulation models is vital in order to define shelf, nearshore and inland hydrodynamics during a hurricane. The intricacies of the inland floodplain domain, level of required mesh resolution and physics make these complex computations very cycle-intensive. Nonetheless, fast wall-clock times are important, especially when forecasting an incoming hurricane. We examine the performance of the unstructured-mesh, SWAN+ADCIRC wave and circulation model applied to a high-resolution, 5M-vertex, finite-element SL16 mesh of the Gulf of Mexico and Louisiana. This multi-process, multi-scale modeling system has been integrated by utilizing inter-model communication that is intra-core. The modeling system is validated through hindcasts of Hurricanes Katrina and Rita (2005), Gustav and Ike (2008) and comprehensive comparisons to wave and water level measurements throughout the region. The performance is tested on a variety of platforms, via the examination of output file requirements and management, and the establishment of wall-clock times and scalability using up to 9,216 cores. Hindcasts of waves and storm surge can be computed efficiently, by solving for as many as 2.3?10¹² unknowns per day of simulation, in as little as 10 minutes of wall-clock time.     

Predictions of typhoon storm surge in Taiwan using artificial neural networks

Accurate predictions of storm surge and surge deviation are essential for industrial activities in coastal areas. Usually numerical hydrodynamic models or empirical methods are used to estimate the storm surge. This paper proposes an alternative back-propagation neural network (BPN) approach to forecast the storm surge and surge deviation. The prediction of storm surge from a previous typhoon is used as a training set to form predictions for the next event. Wind velocity, wind direction, atmospheric pressure and astronomical tide were selected as inputs in the neural network. The observations obtained during three typhoons from four stations in Taiwan were used to illustrate performance of the BPN model. Comparisons with numerical methods indicate that the storm surge and surge deviation can be efficiently predicted using BPN.     

Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes

The shallow water equations are used to model large-scale surface flow in the ocean, coastal rivers, estuaries, salt marshes, bays, and channels. They can describe tidal flows as well as storm surges associated with extreme storm events, such as hurricanes. The resulting currents can transport bed load and suspended sediment and result in morphological changes to the seabed. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations. Discontinuous Galerkin finite element methods are a natural choice for modeling this coupled system, given the need to solve these problems on unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. However, because of the presence of non-conservative products in the momentum equations, the standard DG method cannot be applied in a straightforward manner. To rectify this situation, we summarize and follow an extended approach described by Rhebergen et al., which uses theoretical results due to Dal Maso et al. appearing in earlier work. In this paper, we focus on aspects of the implementation of the morphological model for bed evolution within the Advanced Circulation (ADCIRC) modeling framework, as well as the verification of the RKDG method in both h (mesh spacing) and p (polynomial order). This morphological model is applied to a number of coastal engineering problems, and numerical results are presented, with attention paid to the effects of h- and p-refinement in these applications. In particular, it is observed that for sediment transport, piecewise constant (i.e., finite volume) approximations of the bed are very over-diffusive and lead to poor sediment solutions.     

基于RIA和Skyline的城市风暴潮灾害三维展示系统

风暴潮灾害展示系统可为城市风暴潮灾害辅助决策提供可视化场景和数据应用支持,现有风暴潮灾害系统功能简单,开发技术陈旧。为满足城市风暴潮灾害辅助决策对二维和三维数据展示与分析的需求,依据跨平台、富用户体验和技术新颖的建设目的,设计了城市风暴潮灾害三维展示系统,并以上海浦东新区临港新城数据为例实现了系统应用。介绍城市风暴潮灾害三维展示系统的功能,基于ArcGIS、Skyline TerraSuite、Flex和Java的系统技术框架与建设流程,以及针对三维建模与展示、二维与三维联动及富客户体验等关键问题的解决方案,为城市风暴潮灾害辅助决策相关系统开发提供参考。     

Scalability of an Unstructured Grid Continuous Galerkin Based Hurricane Storm Surge Model

This paper evaluates the parallel performance and scalability of an unstructured grid Shallow Water Equation (SWE) hurricane storm surge model. We use the ADCIRC model, which is based on the generalized wave continuity equation continuous Galerkin method, within a parallel computational framework based on domain decomposition and the MPI (Message Passing Interface) library. We measure the performance of the model run implicitly and explicitly on various grids. We analyze the performance as well as accuracy with various spatial and temporal discretizations. We improve the output writing performance by introducing sets of dedicated writer cores. Performance is measured on the Texas Advanced Computing Center Ranger machine. A high resolution 9,314,706 finite element node grid with 1 s time steps can complete a day of real time hurricane storm surge simulation in less than 20 min of computer wall clock time, using 16,384 cores with sets of dedicated writer cores.     

沿海风暴潮预警预报与灾情评估系统研究

台风是一种严重的自然灾害,引起的风暴增水会对沿海城市产生较大危害,快速准确的风暴潮预警预报及灾情评估是当前研究的热点和难点问题。结合实际业务需求,借鉴类似系统的开发模式,设计提出适用于沿海风暴潮预警预报与灾情评估系统的总体架构,开发预报与评估系统前端主要功能和服务器端相关功能组件,并在广东省进行应用部署。应用结果表明,预报和评估系统实用性和可操作性强,可为沿海防汛部门在台风期的防台会商决策提供强有力的技术支撑。     

风暴潮数值模式的并行化

实现了风暴潮数值模式基于MPI的并行化;根据该模式数值计算的特点提出了一种并行求解三对角方程组的新方法,相对于传统算法编程简单而且并行效率更高;负载平衡是并行程序性能优化首先要解决的问题,以水格点的个数作为任务分解的标准,实现了较好的负载平衡,相比水陆格点不作区分的分解方法性能有明显的提高;在SMP平台上使用8个CPU时加速比可以达到7.0,在集群平台上为6.5。     

Determination of color changes of inks on the uncoated paper with the offset printing during drying using artificial neural networks

This study attempts to determinate color changes based on time in inks applied on the surface of wood-free uncoated paper with offset printing during drying. This study consists of two main cases: (1) Experimental analysis: By preparing a test page according to the 12647-2 principle with an offset printing system, test prints were applied to 120 g/m² wood-free uncoated paper using an ECI 2002 CMYK test chart. Each press was measured being subject to process every 15 min in the first 2 h, then hour by hour between 2 and 12 h, then 4–4 h between 12 and 24 h, and then 6–6 h between 24 and 48 h. CIELAB and reflectance values between 380 and 720 nm of the target, 1,485 colors of the test chart were obtained. To see the drying and color changes of the ink on paper, changes were determined by printing on the paper and applying artificial neural network (ANN) to spectrophotometer data at the stated time intervals. (2) Empirical analysis: The use of the ANN has been proposed as numerical approach to get of empirical equations of color changes in inks applied on the surface of wood-free uncoated paper with offset printing during drying. Based on the outputs of the study, ANN model can be used to estimate the effects of digital proofing systems used in color management on print quality with high confidence with the use of the acquired equations without experimental study. In the study, as colors are defined in terms of wave length, in case, all wave lengths are taken into consideration, certain wave length changes have been taken into consideration.     

MODIS imagery of turbid plumes in San Diego coastal waters during rainstorm events

Data of normalized water-leaving radiance, nLw, obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite at spatial resolution of 250 m (band 1 centered at 645 nm) and 500 m (band 4 at 555 nm) are used to study turbid plumes in coastal waters of southern California during rainstorm events in winter of 2004-2005. Our study area includes San Diego coastal waters, which extend approximately 25 km offshore between Point Loma and 10 km south of the US-Mexican border. These waters are influenced by terrigenous input of particulate and dissolved materials from San Diego and Tijuana watersheds and non-point sources along the shore. Optimum threshold values of satellite-derived normalized water-leaving radiances at both wavebands were established for distinguishing the plume from ambient ocean waters. These threshold values were determined by searching for a maximum correlation between the estimates of satellite-derived plume area calculated using a broad range of nLw values and the environmental variables characterizing rainfall, river discharge, wind, and tides. A correlation analysis involving the amount of precipitated water accumulated during a storm event over the San Diego and Tijuana watersheds was selected as the basis for final determinations of the optimum threshold nLw_thr and subsequent calculations of the plume area. By applying this method to a sequence of MODIS imagery, we demonstrate the spatial extent and evolution of the plume during rainstorm events under various conditions of precipitation, river discharge, wind forcing, and coastal currents.     

Singularity crossing phenomena in DAEs: A two-phase fluid flow application case study

This paper analyzes the existence of smooth trajectories through singular points of differential algebraic equations, or DAEs, arising from traveling wave solutions of a degenerate convection-diffusion model. The DAE system can be written in the quasilinear form A(x)x′ = b(x). In this setting, singularities are displayed when the matrix A(x) undergoes a rank change. The singular hypersurface may be smoothly crossed by trajectories in a finite time if x* is a geometric singularity satisfying certain directional conditions. The basis of our analysis is a two-phase fluid flow model in one spatial dimension with dissipative mechanism involved.     

Predictive Modeling of Coastal Hydrophysical Processes in Multiple-Processor Systems Based on Explicit Schemes

The computational efficiency of implicit and explicit regularized schemes is compared for the suspension transportation and storm surge, which are two actual hydrophysics problems reduced to nonlinear systems of diffusion-convection equations. Regularized schemes are applied to the reformation of the bottom surface caused by the suspension sedimentation on the bottom of the water body under the dumping soil and for modeling the surging storm in the Taganrog Gulf of the Azov Sea on September 24–25, 2014 when the water level exceeded the normal level by 420 cm under the effect of a hurricane that lasted 30 h with a wind speed of 40 m/s. The computational experiments demonstrate that the explicit scheme obtained on a 512-core of a supercomputing system of the Southern Federal University in Taganrog with a computational grid with 5001 × 5001 × 101 nodes is faster by a factor of 71.5 than the implicit scheme.     

Ship motions using single-phase level set with dynamic overset grids

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor-corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr = 0.28 and large, Fr = 0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr = 0.28 and 0.41, with regular linear head waves with slope ak = 0.025 and wavelength λ = 1.5L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case (ak = 0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.     

A multilevel approach for learning from labeled and unlabeled data on graphs

The recent years have witnessed a surge of interest in graph-based semi-supervised learning methods. The common denominator of these methods is that the data are represented by the nodes of a graph, the edges of which encode the pairwise similarities of the data. Despite the theoretical and empirical success, these methods have one major bottleneck which is the high computational complexity (since they usually need to solve a large-scale linear system of equations). In this paper, we propose a multilevel scheme for speeding up the traditional graph based semi-supervised learning methods. Unlike other accelerating approaches based on pure mathematical derivations (like conjugate gradient descent and Lanczos iteration) or intuitions, our method (1) has explicit physical meanings with some graph intuitions; (2) has guaranteed performance since it is closely related to the algebraic multigrid methods. Finally experimental results are presented to show the effectiveness of our method.     

Modelling the influence of irrigated terraces on the hydrological response of a small basin

A geomorphologic-unit-hydrograph based model (H2U) was used to simulate the discharge of the Kali Garang river (Central Java, Indonesia). Even if the peak discharge and concentration time fitted well the observed data, the base time was systematically underestimated. Assuming that the terraced areas delayed part of the streamflow, we first developed a hydraulic model, based on the Cascaded Reservoirs Law, to simulate the outflow of a system of n terraces. This model was calibrated with observed data collected in a three-terrace-system monitoring. Afterwards, the digitized hydrographic network was divided into 2 components: terraced and non-terraced areas. Within the latter, the H2U model simulated directly the transfer to the outlet and it was assumed that the given peak discharge was used to calibrate the global Runoff Coefficient (k_r) of the catchment. Concerning the terraced areas, the delayed outflow computed by the hydraulic model was then routed to the H2U model. The total discharge was given by the sum of the convolutions. The method was applied on the Banyumanik sub-basin (75 km²). The results fit well the observed discharge, even the descending limb. But some more assumptions are needed concerning the way farmers are managing the water within the terraces or the way to assess the average values of the parameters for the entire basin.     

Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations

A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Through discussion and example, parallels are drawn to the tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation issues, scope, and limitations of the software are addressed.

Program summary

Title of program: DDESpecialSolutions.mCatalogue identifier:ADUJProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUJProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format: tar.gzComputers: Created using a PC, but can be run on UNIX and Apple machinesOperating systems under which the program has been tested: Windows 2000 and Windows XPProgramming language used: Mathematica, version 3.0 or higherMemory required to execute with typical data: 9 MBNumber of processors used: 1Has the code been vectorised or parallelized?: NoNumber of lines in distributed program, including test data, etc.: 3221Number of bytes in distributed program, including test data, etc.: 23 745Nature of physical problem: The program computes exact solutions to differential-difference equations in terms of the tanh function. Such solutions describe particle vibrations in lattices, currents in electrical networks, pulses in biological chains, etc.Method of solution: After the differential-difference equation is put in a traveling frame of reference, the coefficients of a candidate polynomial solution in tanh are solved for. The resulting traveling wave solutions are tested by substitution into the original differential-difference equation.Restrictions on the complexity of the program: The system of differential-difference equations must be polynomial. Solutions are polynomial in tanh.Typical running time: The average run time of 16 cases (including the Toda, Volterra, and Ablowitz-Ladik lattices) is 0.228 seconds with a standard deviation of 0.165 seconds on a 2.4 GHz Pentium 4 with 512 MB RAM running Mathematica 4.1. The running time may vary considerably, depending on the complexity of the problem.     

Modelling the fate and transport of negatively buoyant storm–river water in small multi-basin lakes

The dynamics of negatively buoyant river plumes in a small multi-basin kettle lake with steep bathymetry (Toolik Lake, AK) are simulated using a Cartesian hydrodynamic model based on the solution of the three-dimensional shallow water equations. To validate the model, model predictions are compared with results from previous analytical and laboratory studies and with field observations. The grid resolution adopted for the Toolik Lake model is 0.5 m (= Δz) in the vertical and 20 m (= Δx) in the horizontal, so that the ratio of the bottom slope S₀ to Δz/Δx is lower than 4 in 99% of the computational domain. With that resolution, the model represents correctly the rate of mixing between lake and river water and the speed of propagation of downslope gravity currents. The model provides accurate predictions of the temperature structure (RMSE = 0.25 °C) and of eddy diffusivities at the depths of the intrusions of incoming water. Measurements and modelling show similar fractions and depth distribution of river water on a cross-basin transect, which suggests that the mixing dynamics of the plume as it transits between basins are well resolved. Thus, the stage is set to quantify the ecological consequences of storm events in small lakes with several interconnected basins using coupled biological measurements and 3D modelling.