Shallow Water and Navier-Stokes SPH-like numerical modelling of rapidly varying free-surface flows

In coastal engineering, Lagrangian meshless numerical methods have reached a good popularity and they have been applied with success to describe wave breaking, impact of wave on structures and other rapid phenomena. This is due to the fact that they have a number of advantages in comparison with classical Eulerian schemes: no explicit treatment of the free surface and no computational grid mean that sophisticated meshing is not needed for complex geometries and therefore a number of problems that were considered largely intractable using classical Eulerian numerical methods such as finite volume or finite elements can now be simulated. As a relatively new method in Computational Fluid Dynamics, this kind of methods may be considered immature and many fundamental aspects and key characteristics remain to be fully investigated. The solid boundary condition is such an example: imposing closed boundary conditions in meshless methods in general, and in Smoothed Particle Hydrodynamic (SPH) in particular, is still an open problem. In the first chapter of this thesis an approximate Virtual Boundary Particle Method (VBP) for solid boundary conditions in two-dimensional (2-D) SPH models is presented; this is a development of the original VBP method recently proposed by Ferrari et al. (A new 3-D parallel SPH scheme for free-surface flows, Computers \& Fluids, 38(6), 1203-1217, 2009). The aim is to maintain the zeroth moment of the kernel function as closely as possible to unity, (a property referred to as zero-consistency), for particles close to solid boundaries. The main advantage of the MVBP in comparison with other methods such as Mirrored Particles is that curved boundaries or boundaries with angles can be easily reproduced. Some authors applied the Smoothed Particle Hydrodynamics (SPH) method to integrate the Shallow Water Equations (SWE) obtaining promising results for simple test cases where no open boundaries are present and the analytical formulation of source terms are applied: with SPH the wet-dry fronts do not need any special treatment, the equations are solved just where the fluid is present and this can potentially speed up the calculations if there are large dry areas in the domain. A 2D Shallow Water code based on the SPH interpolation is developed in the chapters 2 – 4 of this work, with the aim of further improving the capability of these numerical schemes of simulating real flooding events. The SPH-SWEs code is developed following the variational formulation, thanks to this approach the numerical scheme is robust and both the total mass and the momentum are conserved. Some major improvement has been introduced in the SPH-SWEs model in order to make the simulation of real floodings feasible. The Modified Virtual Boundary Particles (MVBP) is used to describe the closed boundaries, the bottom and the friction source term is described by a set of bottom particle. This discretization is effective not just for simple test case but also in for real bathymetries. Moreover, a particle splitting procedure has been inserted: it has the purpose to avoid the lack of resolution due to the variable kernel size being inversely proportional to water depth. This splitting procedure conserves mass and momentum by varying the smoothing length, velocity and acceleration of each refined particle. This improves predictions but does not necessarily provide good shock capturing. This is improved by treating particle interactions as a Riemann problem with MUSCL reconstruction providing stability. The last limitation that inhibits the use of the SPH-SWEs for real flooding simulation is the absence of any method to impose open boundary conditions. These are introduced in chapter 4 by adopting a simplified version of the Characteristic boundary method. Both supercritical and subcritical inflow and outflow boundary conditions can be simulated. Thanks to all the improvements described above, the simulation of two real events by a SPH-SWEs is presented in chapter 4, for the first time. The first case is the Okushiri tsunami occurred in Japan in 1993, whereas the second one is a flooding flood inundation at Thamesmead (UK). In Chapter 5 the simulation of rapidly varying flows is analysed removing the hypothesis of Shallow Water flows: a meshless Lagrangian numerical model called Finite Pointset Method (FPM) for the integration of Navier-Stokes equations in presence of free-surface flow is presented. The Finite Pointset Method (FPM) is a Lagrangian meshless method for numerical integration of pure incompressible Navier-Stokes equations, applied to date just to internal flows. It belongs to SPH like family because each particle carries a vector of field quantities such as pressure, density, velocity etc. and information and physical quantities are approximated using particles in a circular neighbourhood. FPM holds also some remarkable advantages in comparison with classical SPH methods: it is based on a moving least squares approach, where particles are just interpolation points without any associated mass and this means that any order of accuracy can be reached regardless to the particle’s position. In FPM the fluid is described as purely incompressible and the Navier-Stokes equation are solved numerically by means of the projection method therefore no spurious oscillations in the pressure field are present. Moreover in FPM boundary conditions can be analytically enforced using boundary particles and fluid particles can be added and removed in order to preserve the stability of the solution. This fact represents another fundamental advantage in comparison with classical SPH. Originally the FPM has been confined to single or two phase flow, but in chapter 5 it has extended also to free-surface flows by introducing a novel algorithm for free surface detection. In addition to that, a novel formulation of the Projection Method, called Incremental Pressure Projection Method, has been applied in order to preserve the hydrostatic condition

Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models

Abstract This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow

Experimental and numerical evaluation of the force due to the impact of a dam-break wave on a structure

Flood events caused by the collapse of dams or river levees can have damaging consequences on buildings and infrastructure located in prone areas. Accordingly, a careful prediction of the hydrodynamic load acting on structures is important for flood hazard assessment and potential damage evaluation. However, this represents a challenging task and requires the use of suitable mathematical models. This paper investigates the capability of three different models, i.e. a 2D depth-averaged model, a 3D Eulerian two-phase model, and a 3D Smoothed Particle Hydrodynamics (SPH) model, to estimate the impact load exerted by a dam-break wave on an obstacle. To this purpose, idealised dam-break experiments were carried out by generating a flip-through impact against a rigid squat structure, and measurements of the impact force were obtained directly by using a load cell. The dynamics of the impact event was analyzed and related to the measured load time history. A repeatability analysis was performed due to the great variability typically shown by impact phenomena, and a confidence range was estimated. The comparison between numerical results and experimental data shows the capability of 3D models to reproduce the key features of the flip-through impact. The 2D modelling based on the shallow water approach is not entirely suitable to accurately reproduce the load hydrograph and predict the load peak values; this difficulty increases with the strength of the wave impact. Nevertheless, the error in the peak load estimation is in the order of 10% only, thus the 2D approach may be considered appropriate for practical applications. Moreover, when the shallow water approximation is expected to work well, 2D results are comparable with the experimental data, as well as with the numerical predictions of far more sophisticated and computationally demanding 3D solvers. All the numerical models overestimate the falling limb of the load hydrograph after the impact. The SPH model ensures good evaluation of the long-time load impulse. The 2D shallow water solver and the 3D Eulerian model are less accurate in predicting the load impulse but provide similar results. A sensitivity analysis with respect to the model parameters allows to assess model uncertainty

A GPU-Accelerated Shallow-Water Scheme for Surface Runoff Simulations

The capability of a GPU-parallelized numerical scheme to perform accurate and fast simulations of surface runo in watersheds, exploiting high-resolution digital elevation models (DEMs), was investigated. The numerical computations were carried out by using an explicit finite volume numerical scheme and adopting a recent type of grid called Block-Uniform Quadtree (BUQ), capable of exploiting the computational power of GPUs with negligible overhead. Moreover, stability and zero mass error were ensured, even in the presence of very shallow water depth, by introducing a proper reconstruction of conserved variables at cell interfaces, a specific formulation of the slope source term and an explicit discretization of the friction source term. The 2D shallow water model was tested against two dierent literature tests and a real event that recently occurred in Italy for which field data is available. The influence of the spatial resolution adopted in dierent portions of the domain was also investigated for the last test. The achieved low ratio of simulation to physical times, in some cases less than 1:20, opens new perspectives for flood management strategies. Based on the result of such models, emergency plans can be designed in order to achieve a significant reduction in the economic losses generated by flood events

Un modello 2D con porosit\ue0 per lo studio di allagamenti a larga scala in aree urbane

-Modello 2D con porosit\ue0 per lo studio a larga scala di allagamenti in aree urbane. -Introdotta una formulazione della porosit\ue0 di flusso anisotropa che evita la dipendenza dalla griglia. -Il modello \ue8 in grado di riprodurre la soluzione di riferimento sulla base di soli parametri geometrici. -L\u2019applicazione a casi studio con batimetrie reali \ue8 in fase di sviluppo

Flood inundation modeling in urbanized areas: A mesh-independent porosity approach with anisotropic friction

In the present work, a porosity-based numerical scheme for the Shallow Water Equations is presented. With the aim of accounting for the presence of storage areas, such as gardens, yards and dead zones, and for preferential flow pathways, both an isotropic storage porosity parameter and anisotropic friction are adopted. Particularly, the anisotropic effects due to the building alignments are evaluated defining conveyance porosities along principal directions and using them to express the friction losses in tensor form. The storage and conveyance porosities are evaluated from the geometry of the urban layout at a district scale and then assigned to computational cells rather than to cell sides, thus avoiding oversensitivity to the mesh design. The proposed formulation guarantees the C-property also in presence of wet-dry fronts. Model testing is performed analyzing schematic and idealized urban layouts, and against experimental data as well. The results obtained by the proposed anisotropic scheme are similar to a high-resolution model with resolved buildings, also in the presence of low-friction regimes, meanwhile with a remarkable reduction of the computational times

Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models

This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow.EPSRC, Reino Unido | Ref. EP/L014890/1Ministry of Education, Universities and Research, Italia | Ref. RBSI14R1GPXunta de Galicia | Ref. ED431C 2017/64Ministerio de Economía y Competividad | Ref. ENE2016-75074-C2-1-

Discharge hydrograph estimation at upstream-ungauged sections by coupling a Bayesian methodology and a 2-D GPU shallow water model

Abstract. This paper presents a novel methodology for estimating the unknown discharge hydrograph at the entrance of a river reach when no information is available. The methodology couples an optimization procedure based on the Bayesian geostatistical approach (BGA) with a forward self-developed 2-D hydraulic model. In order to accurately describe the flow propagation in real rivers characterized by large floodable areas, the forward model solves the 2-D shallow water equations (SWEs) by means of a finite volume explicit shock-capturing algorithm. The two-dimensional SWE code exploits the computational power of graphics processing units (GPUs), achieving a ratio of physical to computational time of up to 1000. With the aim of enhancing the computational efficiency of the inverse estimation, the Bayesian technique is parallelized, developing a procedure based on the Secure Shell (SSH) protocol that allows one to take advantage of remote high-performance computing clusters (including those available on the Cloud) equipped with GPUs. The capability of the methodology is assessed by estimating irregular and synthetic inflow hydrographs in real river reaches, also taking into account the presence of downstream corrupted observations. Finally, the procedure is applied to reconstruct a real flood wave in a river reach located in northern Italy

Non-linear wave generation and absorption using open boundaries within DualSPHysics

The present work introduces the implementation of wave generation and wave absorption of non-linear, long-crested regular and irregular waves in the WCSPH-based (Weakly Compressible Smoothed Particle Hydrodynamics) DualSPHysics solver. Open boundaries are applied here for both wave generation and absorption. These boundaries consist of buffer zones, on which physical quantities are imposed, or extrapolated from the fluid domain using ghost nodes. Several layers of buffer particles are used to create an inlet and an outlet, where the horizontal component of the orbital velocities, surface elevation and pressure can be imposed from any external source or extrapolated from the fluid domain. This allows the creation of a numerical wave flume with a length of one wavelength. Reflections within the fluid domain are successfully mitigated using a velocity correction term at both inlet and outlet. The implementation is validated with theoretical solutions, in terms of water surface elevation, wave orbital velocities, and dynamic pressure. The model proves to be capable of propagating waves with less than 5% reflection, and RMSE errors on physical quantities lower than 4.3%. The application of open boundaries proves to be an accurate method to generate and absorb non-linear waves within a restricted domain. © 2019 Elsevier B.V

DualSPHysics: open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH)

DualSPHysics is a hardware accelerated Smoothed Particle Hydrodynamics code developed to solve free-surface flow problems. DualSPHysics is an open-source code developed and released under the terms of GNU General Public License (GPLv3). Along with the source code, a complete documentation that makes easy the compilation and execution of the source files is also distributed. The code has been shown to be efficient and reliable. The parallel power computing of Graphics Computing Units (GPUs) is used to accelerate DualSPHysics by up to two orders of magnitude compared to the performance of the serial version.Research Councils UK (RCUK)Engineering and Physical Sciences Research Council (EPSRC)Ministerio de Economía y Competitividad | Ref. BIA2012-38676-C03-03Xunta de Galici