Shallow Water Equations in Hydraulics: Modeling, Numerics and Applications

This Special Issue aims to provide a forum for the latest advances in hydraulic modeling based on the use of shallow water and related models as well as their novel application in practical engineering. Original contributions, including those in but not limited to the following areas, will be considered for publication: new conceptual models and applications, flood inundation and routing, sediment transport and morphodynamic modelling, pollutant transport in water, irrigation and drainage modeling, numerical simulation in hydraulics, novel numerical methods for the shallow water equations and extended models, case studies, and high-performance computing

Das unstetige Galerkinverfahren für Strömungen mit freier Oberfläche und im Grundwasserbereich in geophysikalischen Anwendungen

Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory. Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing. This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.Für viele geophysikalische Anwendungen spielen Strömungen mit freier Oberfläche und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch für diese Anwendungsszenarien sind große Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit beträchtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten. Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an Flexibilität und sind für paralleles Rechnen gut geeignet. Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher für Strömungen mit freier Oberfläche und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete Stabilitätsanalyse des gekoppelten Modells

Block Fusion on Dynamically Adaptive Spacetree Grids for Shallow Water Waves

Spacetrees are a popular formalism to describe dynamically adaptive Cartesian grids. Even though they directly yield a mesh, it is often computationally reasonable to embed regular Cartesian blocks into their leaves. This promotes stencils working on homogeneous data chunks. The choice of a proper block size is sensitive. While large block sizes foster loop parallelism and vectorisation, they restrict the adaptivity's granularity and hence increase the memory footprint and lower the numerical accuracy per byte. In the present paper, we therefore use a multiscale spacetree-block coupling admitting blocks on all spacetree nodes. We propose to find sets of blocks on the finest scale throughout the simulation and to replace them by fused big blocks. Such a replacement strategy can pick up hardware characteristics, i.e. which block size yields the highest throughput, while the dynamic adaptivity of the fine grid mesh is not constrained—applications can work with fine granular blocks. We study the fusion with a state-of-the-art shallow water solver at hands of an Intel Sandy Bridge and a Xeon Phi processor where we anticipate their reaction to selected block optimisation and vectorisation

A UPC++ Actor Library and Its Evaluation on a Shallow Water Proxy Application

Programmability is one of the key challenges of Exascale Computing. Using the actor model for distributed computations may be one solution. The actor model separates computation from communication while still enabling their over-lap. Each actor possesses specified communication endpoints to publish and receive information. Computations are undertaken based on the data available on these channels. We present a library that implements this programming model using UPC++, a PGAS library, and evaluate three different parallelization strategies, one based on rank-sequential execution, one based on multiple threads in a rank, and one based on OpenMP tasks. In an evaluation of our library using shallow water proxy applications, our solution compares favorably against an earlier implementation based on X10, and a BSP-based approach

New prospects for computational hydraulics by leveraging high-performance heterogeneous computing techniques

In the last two decades, computational hydraulics has undergone a rapid development following the advancement of data acquisition and computing technologies. Using a finite-volume Godunov-type hydrodynamic model, this work demonstrates the promise of modern high-performance computing technology to achieve real-time flood modeling at a regional scale. The software is implemented for high-performance heterogeneous computing using the OpenCL programming framework, and developed to support simulations across multiple GPUs using a domain decomposition technique and across multiple systems through an efficient implementation of the Message Passing Interface (MPI) standard. The software is applied for a convective storm induced flood event in Newcastle upon Tyne, demonstrating high computational performance across a GPU cluster, and good agreement against crowd- sourced observations. Issues relating to data availability, complex urban topography and differences in drainage capacity affect results for a small number of areas

Lattice Boltzmann modeling for shallow water equations using high performance computing

The aim of this dissertation project is to extend the standard Lattice Boltzmann method (LBM) for shallow water flows in order to deal with three dimensional flow fields. The shallow water and mass transport equations have wide applications in ocean, coastal, and hydraulic engineering, which can benefit from the advantages of the LBM. The LBM has recently become an attractive numerical method to solve various fluid dynamics phenomena; however, it has not been extensively applied to modeling shallow water flow and mass transport. Only a few works can be found on improving the LBM for mass transport in shallow water flows and even fewer on extending it to model three dimensional shallow water flow fields. The application of the LBM to modeling the shallow water and mass transport equations has been limited because it is not clearly understood how the LBM solves the shallow water and mass transport equations. The project first focuses on studying the importance of choosing enhanced collision operators such as the multiple-relaxation-time (MRT) and two-relaxation-time (TRT) over the standard single-relaxation-time (SRT) in LBM. A (MRT) collision operator is chosen for the shallow water equations, while a (TRT) method is used for the advection-dispersion equation. Furthermore, two speed-of-sound techniques are introduced to account for heterogeneous and anisotropic dispersion coefficients. By selecting appropriate equilibrium distribution functions, the standard LBM is extended to solve three-dimensional wind-driven and density-driven circulation by introducing a multi-layer LB model. A MRT-LBM model is used to solve for each layer coupled by the vertical viscosity forcing term. To increase solution stability, an implicit step is suggested to obtain stratified flow velocities. Numerical examples are presented to verify the multi-layer LB model against analytical solutions. The model’s capability of calculating lateral and vertical distributions of the horizontal velocities is demonstrated for wind- and density- driven circulation over non-uniform bathymetry. The parallel performance of the LBM on central processing unit (CPU) based and graphics processing unit (GPU) based high performance computing (HPC) architectures is investigated showing attractive performance in relation to speedup and scalability

Optimal control for studying wave energy in hydraulic systems

A class of novel models for water waves induced by elastic deformation in the topography is developed and analyzed. The depth-averaged shallow water equations including friction terms for the water free-surface and the well-known second-order elastostatic formulation for the bed deformation have been implemented. Friction forces and water hydrostatic pressure distribution are also accounted for in this model. At the interface between the water ow and the bed topography, transfer conditions are implemented. Furthermore, a hybrid nite element/nite volume method for solving free-surface run-up ow problems over deformable beds has been proposed. The deformations in the topography have been generated by a localized force which causes propagations of the water waves with dierent amplitudes and frequencies. Two dierent methods have been proposed for the transfer of informations through the interface. The rst one is the two-mesh procedure; in this method a proper interpolation has been implemented to transfer the data between the surface nodes and the control volumes using uniform nite volume meshes. In the second method, and to avoid the interpolation at the interface, a nite volume method using non-uniform meshes has been implemented. When the shallow water waves approach the coastline they begin to transform as they enter shallow water regime. As each wave begins to experience the seabed, both run-up and overtopping occur. To solve for this, a class of stable, accurate and simple numerical model for moving wet/dry fronts in shallow water equations using the parametrization concept and the point-wise Riemann solver has been proposed. Many parameters of shallow water equations are subject to uncertainties to the inherit randomness of natural processes. To incorporate uncertain parameters into the stochastic shallow water equations, the stochastic properties of dierent parameters that are considered uncertain, namely in ow boundary condition, the bed friction coecients and the domain topography are added to the system. Development of accurate and ecient tools for uncertainty quantication in shallow water ows has been proposed and carefully examined for single-layer, two-layer - nite volume models. To further quantify the uncertainty in shallow water ows the proposed methods have been extended to multi-layer shallow water ows with mass exchange terms subject to stochastic topography, uncertain friction and viscosity coecients. Several test examples and well-established benchmark problems have been used to assess the numerical performance of the proposed models and methods. Comparisons to experimental measurements have also been carried out in this thesis. Finally, an optimal control technique for bed reconstruction has been presented as in many engineering applications this information is not entirely provided