Search Results (36)

The shallow water equations (SWEs) model fluid flow in rivers, coasts, and tsunamis. Their nonlinearity challenges analytical solutions. We present a numerical algorithm combining the finite integration method with Chebyshev polynomial expansion (FIM-CPE) to solve one- and two-dimensional SWEs. The method transforms partial differential equations into integral equations, approximates spatial terms via Chebyshev polynomials, and uses forward differences for time discretization. Validated on stationary lakes, dam breaks, and Gaussian pulses, the scheme achieved errors below ${10}^{-12}$ for water height and velocity, while conserving mass with volume deviations under ${10}^{-5}$. Comparisons showed superior shock-capturing versus finite difference methods. For two-dimensional cases, it accurately resolved wave interactions over complex topographies. Though limited to wet beds and small-scale two-dimensional problems, the method provides a robust simulation tool. Full article

In 2071, the Hydraulic community will commemorate the second centenary of the Baré de Saint-Venant equations, also known as the Shallow Water Equations (SWE). These equations are fundamental to the study of open-channel flow. As non-linear partial differential equations, their solutions were largely unattainable until the development of computers and numerical methods. Following 1960, various numerical schemes emerged, with Preissmann’s scheme becoming the most widely employed in many software applications. In the 1990s, some researchers identified a significant limitation in existing software and codes: the inability to simulate transcritical flow. At that time, Preissmann’s scheme was the dominant method employed in hydraulics tools, leading the research community to conclude that this scheme could not handle transcritical flow due to suspected instability. In response to this concern, several researchers suggested modifications to Preissmann’s scheme to enable the simulation of transcritical flow. This paper will demonstrate that these accusations against the Preissmann scheme are unfounded and that the proposed improvements are unnecessary. The observed instability is not due to the numerical method itself, but rather a mathematical instability inherent to the SWE, which can lead to ill-posed conditions if a specific derived condition is not met. In the context of a friction slope formula based on Manning or Chézy types, the condition for ill-posedness of the 1D shallow water equations simplifies to the Vedernikov number condition, which is necessary for roll waves to develop in uniform flow. This derived condition is also relevant for the formation of roll waves in unsteady flow when the 1D shallow water equations become ill-posed. Full article

Extreme rainstorms are difficult to predict and often result in catchment-scale rainfall flooding, leading to substantial economic losses globally. Enhancing the numerical computational efficiency of flood models is essential for improving flood forecasting capabilities. This study presents an integrated hydrological–hydrodynamic model accelerated using GPU (Graphics Processing Unit) technology to perform high-efficiency and high-precision rainfall flood simulations at the catchment scale. The model couples hydrological and hydrodynamic processes by solving the fully two-dimensional shallow water equations (2D SWEs), incorporating GPU-accelerated parallel computing. The model achieves accelerated rainstorm flooding simulations through its implementation on GPUs with parallel computing technology, significantly enhancing its computational efficiency and maintaining its numerical stability. Validations are conducted using an idealized V-shaped catchment and an experimental benchmark, followed by application to a small catchment on the Chinese Loess Plateau. The computational experiments reveal a strong positive correlation between grid cell numbers and GPU acceleration efficiency. The results also demonstrate that the proposed model offers better computational accuracy and acceleration performance than the single-GPU model. This GPU-accelerated hydrological–hydrodynamic modeling framework enables rapid, high-fidelity rainfall flood simulations and provides critical support for timely and effective flood emergency decision making. Full article

Godunov-based finite volume (FV) methods are widely employed to numerically solve the Shallow-Water Equations (SWEs) with application to simulate flood inundation over irregular geometries and real-field, where unstructured triangular meshing is favored. Second-order extensions have been devised, mostly on the MUSCL reconstruction and the discontinuous Galerkin (DG) approaches. In this paper, we introduce a novel second-order Runge–Kutta discontinuous Galerkin (RKDG) solver for flood modeling, specifically addressing positivity preservation and wetting and drying on unstructured triangular meshes. To enhance the RKDG model, we adapt and refine positivity-preserving and wetting and drying techniques originally developed for the MUSCL-based finite volume (FV) scheme, ensuring its effective integration within the RKDG framework. Two analytical test problems are considered first to validate the proposed model and assess its performance in comparison with the MUSCL formulation. The performance of the model is further explored in real flooding scenarios involving irregular topographies. Our findings indicate that the added complexity of the RKDG model is justified, as it delivers higher-quality results even on very coarse meshes. This reveals that there is a promise in deploying RKDG-based flood models in real-scale applications, in particular when field data are sparse or of limited resolution. Full article

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, this method uses the differential transformation (DT) procedure rather than the traditional Cauchy–Kowalewski (CK) procedure to achieve the local temporal evolution. Compared with the classical ADER methods, the current method is free of solving generalized Riemann problems at inter-cells. In comparison with the Runge–Kutta DG (RKDG) methods, the proposed method needs less computer storage, thanks to the absence of intermediate stages. In brief, this current method is one-step, one-stage, and fully-discrete. Moreover, this method can easily obtain arbitrary high-order accuracy both in space and in time. Numerical results for one- and two-dimensional shallow water equations (SWEs) show that the method enjoys high-order accuracy and keeps good resolution for discontinuous solutions. Full article

This article presents a methodology for evaluating the susceptibility of landfill areas to develop landslides by analyzing Synthetic Aperture Radar (SAR) satellite products. The deformation velocity of the landfills is computed through the Persistent Scatterer Method on SAR imagery. These data, combined with a deformation model based on the shallow water equations (SWE), form the foundation for a Monte Carlo experiment that extrapolates the current state of the landfill into the future. The results of this simulation are then employed to determine the probability of a landslide occurrence. In order to validate the methodology effectiveness, a case study is conducted on a landfill in Zaldibar, Spain, revealing its effectiveness in estimating the probability of landfill landslides. This innovative approach emerges as an asset in large landfill management, acting as a proactive tool for identifying high-risk sites and preventing potential landslides, ultimately safeguarding human life and the environment. By providing insights into landslide probabilities, this study enhances decision-making processes and facilitates the development of intervention strategies in the domain of landfill risk assessment and management. Full article

In recent years, mountainous areas in China have faced frequent geological hazards, including landslides, debris flows, and collapses. Effective simulation of these events requires a solver for shallow water equations (SWEs). Traditional numerical methods, such as finite difference and finite volume, face challenges in discretizing convection flux terms, while theory-based models need to account for various factors such as shock wave capturing and wave propagation direction, demanding a high-level understanding of the underlying physics. Previous deep learning (DL)-based SWE solvers primarily focused on constructing direct input–output mappings, leading to weak generalization properties when terrain data or stress constitutive relations change. To overcome these limitations, this study introduces a novel SWE solver that combines theory and data-driven methodologies. The core idea is to use artificial neural networks to compute convection flux terms, and to reduce modeling complexity. Theory-based modeling is used to tackle complex terrain and friction terms for the purpose of ensuring generalization. Our method surpasses challenges faced by previous DL-based solvers in capturing terrain and stress variations. We validated our solver’s capabilities by comparing simulation results with analytical solutions, real-world disaster cases, and the widely used Massflow software-generated simulations. This comprehensive comparison confirms our solver’s ability to accurately simulate hazard scenarios and showcases strong generalization on varying terrain and land surface friction. Our proposed method effectively addresses DL-based solver limitations while simplifying the complexities of theory-driven numerical methods, offering a promising approach for hazard dynamics simulation. Full article

Here we present the numerical methods, applications, and comparisons with observations and previous studies. It includes numerical analyses of shallow water equations, Sun’s scheme, and nonlinear model simulations of a dam break, solitary Rossby wave, and hydraulic jump without smoothing. We reproduce the longitude and transverse cloud bands in the Equator; two-day mesoscale waves in Brazil; Ekman spirals in the atmosphere and oceans, and a resonance instability at 30° from the linearized equations. The Purdue Regional Climate Model (PRCM) reproduces the explosive severe winter storms in the Western USA; lee-vortices in Taiwan; deformation of the cold front by mountains in Taiwan; flooding and drought in the USA; flooding in Asia; and the Southeast Asia monsoons. The model can correct the small-scale errors if the synoptic systems are correct. Usually, large-scale systems are more important than small-scale disturbances, and the predictability of NWP is better than the simplified dynamics models. We discuss the difference between Boussinesq fluid and the compressible fluid. The Bernoulli function in compressible atmosphere conserving the total energy, is better than the convective available potential energy (CAPE) or the Froude number, because storms can develop without CAPE, and downslope wind can form against a positive buoyancy. We also present a new terrain following coordinate, a turbulence-diffusion model in the convective boundary layer (CBL), and a new backward-integration model including turbulence mixing in the atmosphere. Full article

This paper is to investigate the capability of six numerical schemes to simulate reflected wave over a dry and closed domain with and without building, namely: (a) two proposed 2D numerical models solving the conservation form of 2D Shallow Water Equations (2D-SWEs) by Finite Volume Method (FVM) with Roe and HLLC schemes are invoked to approximate Reimann solver; (b) three options of shallow models in the commercial software Flow 3D based on a non-conservation form of 2D-SWEs and (c) the Flow 3D with turbulence modules. By analyzing flooding maps, the area of the reflected wave, and water level profiles on a dry and closed domain, two proposed models give reasonable solutions, while three options of the shallow module of Flow 3D originate result less accurately when initial wave celerity (c₀) is small. The accuracy level will be increased if c₀ value increases. The 3D model presented the best performance of the complex flow pattern in the dry and enclosed domain in both cases without and with building. Full article

The computational simulation of rivers is a useful tool that can be applied in a wide range of situations from providing real time alerts to the design of future mitigation plans. However, for all the applications, there are two important requirements when modeling river behavior: accuracy and reasonable computational times. This target has led to recent developments in numerical models based on the full two-dimensional (2D) shallow water equations (SWE). This work presents a GPU accelerated 2D SW model for the simulation of flood events in real time. It is based on a well-balanced explicit first-order finite volume scheme able to run over dry beds without the numerical instabilities that are likely to occur when used in complex topography. The model is applied to reproduce a real event in the reach of the Ebro River (Spain) with a downstream reservoir, in which a study of the most appropriate boundary condition (BC) for modeling of the dam is assessed (time-dependent level condition and weir condition). The whole creation of the model is detailed in terms of mesh optimization and validation. The simulation results are compared with field data over the flood duration (up to 20 days), allowing an analysis of the performance and time saved by different GPU devices and with the different BCs. The high values of fit between observed and simulated results, as well as the computational times achieved, are encouraging to propose the use of the model as a forecasting system. Full article

The precision of numerical overland flow models is limited by their computational cost. A GPU-accelerated 2D shallow flow model is developed to overcome this challenge in this study. The model employs a Godunov-type finite volume method (FVM) to solve shallow water equations (SWEs) with unstructured grids, while also considering rainfall, infiltration, bottom slope, and friction source terms. The numerical simulation demonstrates that this model has well-balanced and robust properties. In an experiment of urban rain-runoff and flood, the accuracy and stability of the model are further demonstrated. The model is programmed with CUDA, and each numerical computation term is processed in parallel to adopt multi-thread GPU acceleration technology. With the GPU computation framework, this model can achieve a speeding up ration around 75 to single-thread CPU in the dam-break flow for a large-scale application. Full article

The numerical modeling of actual river floods faces three challenges related to computational efficiency, accuracy, and proper balancing of terms in the governing equations, all of which are discussed in this paper. Herein, a large time step (LTS) scheme is used to improve efficiency, a high order scheme is used to enhance accuracy, and specific treatment of the bed slope term achieves a well-balanced form of shallow water equations. The LTS scheme, originally proposed by LeVeque in 1998, has led to the development of highly efficient computational solvers of the shallow water equations (SWEs). This paper examines use of a total variation diminishing (TVD) high order scheme in conjunction with LTS. We first applied the scheme to the solution of the homogeneous 1D SWEs and obtained satisfactory results for three cases, even though small oscillations nevertheless occur when the CFL number is very large. The additional source term makes the issue more complicated and can introduce a spurious flow when the term is not correctly handled. Many methods have been developed in traditional differential schemes, but not all are fit for the TVD-LTS scheme; for example, the method of decomposing the source term into simple characteristic waves has proved infeasible. In this paper the TVD-LTS scheme was implemented for the first time for well-balanced SWEs containing bed slope source terms. We found that oscillations were not as suppressed as for the homogeneous SWEs when the TVD-LTS scheme was applied to the three cases of step Riemann problems (SRP) tested for CFL numbers 1 to 10. For free surface flow over a bed hump, the TVD-LTS scheme can only reach CFL number 4 before the solution breaks down. Full article

Marine debris is an important environmental problem that affects aquatic animals, ecosystems, economy, society, and humans. This research aims to simulate the path of marine debris in the Gulf of Thailand using a mathematical model that includes two models: the Oceanic Model (OCM), which is based on the Shallow Water Equations (SWE), and the Lagrangian Particle Tracking (LPT) model. The OCM is the partial derivative equation system solved by the finite difference method to satisfy the Arakawa C-grid and the splitting method. The LPT model includes the current velocity, wind velocity at 10 m above sea level, random walk term, and the buoyancy ratio of marine debris with six cases, which are 100:1, 10:1, 1:1, 0:1, 1:10, and 1:100. The current velocity from OCM is applied to the LPT model. This research uses a garbage boat that capsized near Koh Samui on 1 August 2020 as a case study. The simulated current velocity of OCM is compared with Ocean Surface Current Analyses Real-time (OSCAR) data. The Root Mean Square Error (RMSE) of u-velocity is 0.070 m/s, and that of v-velocity is 0.058 m/s. The simulation of the marine debris’s path from the LPT model demonstrates the movement to Koh Samui, Koh Taen, Koh Wang Nai, Koh Wang Nok, Koh Rap, the east coast of Nakorn Si Thammarat province, Phu Quoc Island of Vietnam and the middle of the Gulf of Thailand with the different buoyancy ratios and time durations. Full article

We pose the following research question, “what are (i) the minimum required computation grid and (ii) the required form of hydrodynamic equations, i.e., shallow water equations (SWE) or diffusion wave equations (DWE), in 2D modeling to minimize the computational time while maintaining an acceptable level of error in the prediction of water depths and the extent of flood inundated areas?”. To answer this question, we apply the HEC-RAS 1D/2D model to simulate a disastrous flash flood in the town of Mandra, in Attica, Greece, in November 2017. HEC-RAS 1D/2D combines 1D modeling in the cross-sections of the two main streams of Mandra with 2D modeling in the rest of the potentially flooded area of the computational domain which has an area equal to 18.36 km². We perform calculations for 8 scenarios that combined various grid sizes (with approximately 44,000–95,000 control volumes) with the use of the SWE or DWE. We derive the following conclusions: (i) calculated maximum water depths using DWE were equal to 60–65% of the corresponding water depths using SWE, i.e., the DWE significantly underestimated water depths; (ii) calculated total inundation areas using the SWE were approximately 4.9–7.9% larger than the corresponding inundation areas using the DWE; these differences can be considered as acceptable; and (iii) the total computation times using SWE, which ranged from 67 to 127 min, were 60–70% longer than the computation times using DWE. Full article

Hydroplaning risk evaluation plays a pivotal role in highway safety management. It is also an important component in the intelligent transportation system (ITS) ensuring human driving safety. Water-film is the widely accepted vital factor resulting in hydroplaning and thus continuously gained researchers’ attention in recent years. This paper provides a new framework to evaluate the hydroplaning potential based on emerging 3D laser scanning technology and water-film thickness estimation. The 3D information of the road surface was captured using a vehicle-mounted Light Detection and Ranging (LiDAR) system and then processed by a wavelet-based filter to remove the redundant information (surrounding environment: trees, buildings, and vehicles). Then, the water film thickness on the given road surface was estimated based on a proposed numerical algorithm developed by the two-dimensional depth-averaged Shallow Water Equations (2DDA-SWE). The effect of the road surface geometry was also investigated based on several field test data in Shanghai, China, in January 2021. The results indicated that the water-film is more likely to appear on the rutting tracks and the pavement with local unevenness. Based on the estimated water-film, the hydroplaning speeds were then estimated to represent the hydroplaning risk of asphalt pavement in rainy weather. The proposed method provides new insights into the water-film estimation, which can help drivers make effective decisions to maintain safe driving. Full article