► Novel SPH variable variationally derived algorithm with variable resolution included. ► Particle splitting and coalescing (merging) procedures. ► Particle shifting procedures for treating domains ...with variable mass particles. ► Testing against analytical solution for Poiseuille and Taylor–Green flows (including convergence analysis). ► Speed-ups of about 5, while maintaining the same level of accuracy as a uniform distribution with most refined resolution.
In this paper a novel variable resolution method using particle splitting and coalescing for the SPH numerical solution of the Navier–Stokes equations is presented. The key idea of the scheme is to modify dynamically the particle sizes by means of splitting and coalescing (merging) individual particles to provide good resolution only where it is needed. The SPH scheme adopted is derived using the variational principle guaranteeing that both mass and momentum are conserved for particles with different smoothing lengths. A particle shifting procedure is used to prevent unacceptable anisotropic distributions of the particles and is further generalized for treating domains with variable mass particles. The algorithm has been tested against analytical solutions for Poiseuille and Taylor–Green flows showing that the shifting algorithm is effective in increasing the accuracy, and that error introduced by the splitting and coalescing is negligible. The capability of the numerical scheme for increasing efficiency is shown for more general problems: the simulations of a moving square in a box and flow past a cylinder have shown that the particle refinement procedure is able to increase the efficiency while maintaining the same level of accuracy as a uniform distribution with the most refined resolution.
•3D numerical modeling of the wave generated by the Vajont rockslide.•Definition of the rocklide kinematics using a 3D approach.•Parallel 3D SPH numerical scheme obtained using the Compute Unified ...Device Architecture (CUDA) of nVidia devices.•Validation against data available in literature.
A 3D numerical modeling of the wave generated by the Vajont slide, one of the most destructive ever occurred, is presented in this paper. A meshless Lagrangian Smoothed Particle Hydrodynamics (SPH) technique was adopted to simulate the highly fragmented violent flow generated by the falling slide in the artificial reservoir. The speed-up achievable via General Purpose Graphic Processing Units (GP-GPU) allowed to adopt the adequate resolution to describe the phenomenon. The comparison with the data available in literature showed that the results of the numerical simulation reproduce satisfactorily the maximum run-up, also the water surface elevation in the residual lake after the event.
Moreover, the 3D velocity field of the flow during the event and the discharge hydrograph which overtopped the dam, were obtained.
This paper presents a two‐dimensional shallow water equations code coupled with a physically based erosion model, able to predict the opening and evolution of breaches forming in levees built with ...either cohesive or noncohesive material. The bottom elevation change is evaluated using an excess shear‐stress equation, which accounts for the hydrodynamic conditions and for the material characteristics. The proposed model modifies the local topography at runtime wherever the levee is overtopped without having to predefine the position and shape of the breach. The model is implemented in CUDA programming language, so that simulations can be run on graphics processing units, guaranteeing fast execution times even for high‐resolution meshes and large domains. The validation is performed based on several experimental tests, and numerical predictions are in good agreement with the measurements. The strengths and weaknesses of the proposed approach are also discussed by comparison with a sediment transport model based on the Exner equation: While the latter gives good results only for breaches forming in levees built with noncohesive material, the proposed model can also be applied to cohesive embankments. The application to a historical flood event is also presented, showing that the model can effectively be employed for real field simulations also in the case of multiple breaches.
Key Points
The paper presents a 2D SWE model able to simulate the opening of a levee breach due to overtopping and the subsequent flooding
The physically based erosion model allows predicting the breach evolution in levees made of cohesive or noncohesive material
The model can be applied to real cases, thanks to the fast execution times guaranteed by the GPU parallelization of computations
In this paper a parallelization of a Shallow Water numerical scheme suitable for Graphics Processor Unit (GPU) architectures under the NVIDIA™'s Compute Unified Device Architecture (CUDA) framework ...is presented. In order to provide robust and accurate simulations of real flood events, the system features a state-of-the-art Finite Volume explicit discretization technique which is well balanced, second order accurate and based on positive depth reconstruction. The model is based on a Cartesian grid and boundary conditions are implemented by means of the implicit local ghost cell approach, which enables the discretization of a broad spectrum of boundary conditions including inflow/outflow conditions. A novel and efficient Block Deactivation Optimization procedure has also been adopted, in order to increase the efficiency of the numerical scheme in the presence of wetting-drying fronts. This led to speedups of two orders of magnitude with respect to a single-core CPU. The code has been validated against several severe benchmark test cases, and its capability of producing accurate fast simulations (with high ratios between physical and computing times) for different real world cases has been shown.
•Shallow Water Equations parallel numerical scheme suitable for GPU.•Speedup of two order of magnitude over a single-core CPU.•Robust treatment of wetting and drying fronts.•Optimization strategies for partially dry domains.•Real-life simulations with open and closed boundaries.
Summary
This paper presents a numerical strategy based on shallow water equations (SWE) coupled with the 2D Preissmann slot model to handle a ceiling step discontinuity in finite volume schemes for ...mixed flow modeling. In practice, a typical situation would be a closed structure, such as a bridge or culvert, which induces a sudden vertical flow constriction and may even run partly or totally full in high flow conditions. In such case, both the inlet and outlet of the structure involve a discontinuity in the top elevation. This special singularity is topologically represented by inserting a fictitious cell between 2 adjacent computational cells characterized by sharply different ceiling elevation. The 2D SWE are solved by means of a well‐balanced quasi‐conservative Godunov‐type numerical scheme based on the Slope Limiter Centered (SLIC) scheme. The flow variables at each boundary of the fictitious cell are reconstructed by adopting the cross‐sectional shape of the adjoining cell. Accordingly, the dynamic effect of the structure deck on the flow is suitably modeled, and the C‐property for a stationary solution is rigorously satisfied, even when the closed structure is partially full. The capability of the numerical scheme is verified by comparison with both novel analytical solutions of 1D Riemann problems with a ceiling step discontinuity and experimental data of steady and unsteady mixed flows available in literature. Finally, a real‐scale application to a multiple arch bridge is presented. The results show that the method is robust and effective in predicting the 2D features induced by a crossing structure on the flow dynamics.
We propose a numerical method based on the 2D Preissmann slot model to treat a ceiling step discontinuity in shallow water mixed flow modeling. The singularity in the top surface elevation is represented by inserting a fictitious cell, and the 2D shallow water equations are solved by means of a well‐balanced quasi‐conservative Godunov‐type finite volume numerical scheme. The results show that the method is robust and effective in predicting the 2D features induced by a crossing structure on the flow dynamics.
AbstractA smoothed particle hydrodynamics (SPH) numerical model for shallow water equations (SWEs) is presented for simulating flood inundation owing to rapidly varying flow, such as dam breaks, ...tsunamis, and levee breaches. Important theoretical and numerical developments have recently been made, and the model in this paper incorporates these developments and implements open boundary conditions, resulting in a general, accurate computational tool suitable for practical application. The method is attractive for flood simulation over large domains in which the extent of inundation is unknown because computation is carried out only in wet areas and is dynamically adaptive. The open boundary algorithm is very general, on the basis of a simplified version of the characteristics method, handling both supercritical and subcritical inflow and outflow. This is tested against reference solutions for flows over a hump involving shocks. The model is then applied to two very different flood inundations resulting from the Okushiri tsunami in Japan and from a hypothetical dyke breach at Thamesmead in the United Kingdom. The SPH-SWE model compares well with established commercial and state-of-the-art finite-volume codes.
A finite volume MUSCL scheme for the numerical integration of 2D shallow water equations is presented. In the framework of the SLIC scheme, the proposed weighted surface-depth gradient method (WSDGM) ...computes intercell water depths through a weighted average of DGM and SGM reconstructions, in which the weight function depends on the local Froude number. This combination makes the scheme capable of performing a robust tracking of wet/dry fronts and, together with an unsplit centered discretization of the bed slope source term, of maintaining the static condition on non-flat topographies (C-property). A correction of the numerical fluxes in the computational cells with water depth smaller than a fixed tolerance enables a drastic reduction of the mass error in the presence of wetting and drying fronts. The effectiveness and robustness of the proposed scheme are assessed by comparing numerical results with analytical and reference solutions of a set of test cases. Moreover, to show the capability of the numerical model on field-scale applications, the results of a dam-break scenario are presented.
•SPH h-variable algorithm for Shallow Water Equations with variable resolution.•Dynamic particle splitting and coalescing (merging) conservative procedures.•Testing against analytical solutions and ...experimental data.•Application to a practical test case, obtaining a speed-ups of about 15.
In this paper an adaptive algorithm for Smoothed Particle Hydrodynamics (SPH) for the Shallow Water Equations (SWEs) is presented. The area of a particle is inversely proportional to depth giving poor resolution in small depths without particle refinement. This is a particular limitation for flooding problems of interest here. Higher resolution is created by splitting the particles, while particle coalescing (or merging) improves efficiency by reducing the number of the particles when acceptable. The new particle coalescing procedure merges two particles together if their area becomes less than a predefined threshold value. Both particle splitting and coalescing procedures conserve mass and momentum and the smoothing length of new particles is calculated by minimizing the density error of the SPH summation. The new dynamic particle refinement procedure is assessed by testing the numerical scheme against analytical, experimental and benchmark test cases. The analytical cases show that with particle splitting and coalescing typical convergence rates remain faster than linear. For the practical test case, in comparison to using particle splitting alone, the particle coalescing procedure leads to a significant reduction of computational time, by a factor of 15. This makes the computational time of the same order as mesh-based methods with the advantage of not having to specify a mesh over a flood domain of unknown extent a priori.
With the aim of improving resilience to flooding and increasing preparedness to face levee-breach-induced inundations, this paper presents a methodology for creating a wide database of numerically ...simulated flooding scenarios due to embankment failures, applicable to any lowland area protected by river levees. The analysis of the detailed spatial and temporal flood data obtained from these hypothetical scenarios is expected to contribute both to the development of civil protection planning and to immediate actions during a possible future flood event (comparable to one of the available simulations in the database) for which real-time modelling may not be feasible. The most relevant criteria concerning the choice of mathematical model, grid resolution, hydrological conditions, breach parameters and locations are discussed in detail.
The proposed methodology, named RESILIENCE, is applied to a 1100 km2 pilot area in northern Italy. The creation of a wide database for the study area is made possible thanks to the adoption of a GPU-accelerated shallow-water numerical model which guarantees remarkable computational efficiency (ratios of physical to computational time up to 80) even for high-resolution meshes (2.5–5 m) and very large domains (>1000 km2).
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