Modeling Flow Encountering Abrupt Topography Using Hybridizable Discontinuous Galerkin Projection Methods

In this work novel high-order hybridizable discontinuous Galerkin (HDG) projection methods are further developed for ocean dynamics and geophysical fluid predictions. We investigate the effects of the HDG stabilization parameter for both the momentum equation as well as tracer diffusion. We also make a correction to our singularity treatment algorithm for nailing down a numerically consistent and unique solution to the pressure Poisson equation with homogeneous Neumann boundary conditions everywhere along the boundary. Extensive numerical results using physically realistic ocean flows are presented to verify the HDG projection methods, including the formation of internal wave beams over a shallow but abrupt seamount, the generation of internal solitary waves from stratified oscillatory flow over steep topography, and the circulation of bottom gravity currents down a slope. Additionally, we investigate the implementation of open boundary conditions for finite element methods and present results in the context of our ocean simulations. Through this work we present the hybridizable discontinuous Galerkin projection methods as a viable and competitive alternative for large-scale, realistic ocean modeling.

Replacing the Traditional Physical Model Approach Computational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fields of science and engineering, its use for hydraulics has so far been limited to simple cases. The book compares numerical results with laboratory experiments and field data, and includes a set of tests that can be used for a wide range of applications. Provides step-by-step implementation details Presents the different forms in which the shallow water flow equations can be written Places emphasis on the details and modifications required to apply the scheme to real-world flow problems This text enables readers to readily understand and develop an efficient computer simulation model that can be used to model flow, contaminant transport, and other aspects in rivers and coastal environments. It is an ideal resource for practicing environmental engineers and researchers in the area of computational hydraulics and fluid dynamics, and graduate students in computational hydraulics.

This thesis presents the development and application of a multidimensional (2-D & 1-D) kinematic wave model in a discontinuous Galerkin framework for simulating overland flow and runoff due to torrential rainfall. The objective of this work is to improve on (1) the modeling approach involving many small-scale rivers and channels and (2) the accuracy of flooding caused by storm surge coupled with torrential rainfall. The overland flow is modeled using the 2-D kinematic wave equations derived from the 2-D depth averaged shallow water equations. In areas of the domain where flow converges into channels, the edges of 2-D elements are used as 1-D channels for flow routing. To best represent complex topography, domains are discretized using an application co-developed by the author called Admesh+, an automatic unstructured mesh generator for shallow water models. Admesh+ produces high-quality meshes with the appropriate amount of refinement where it is needed to resolve all of the geometry and flow characteristics of the domain. The mesh generation technique utilizes high-resolution digital elevation maps (DEMs) to automatically produce unstructured meshes with elements arranged to best represent shorelines, channel networks and watershed delineations. The development of the multidimensional overland flow model and mesh generation techniques are presented along with comparisons of model results with various analytic solutions and experimental data.

As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD) tools in aerospace and research facilities are widely used to evaluate the aerodynamic performance of aircraft or wings. Weather forecasts are highly dependent on numerical weather prediction (NWP) model. However, it is still difficult to simulate the complex physical phenomena of a wide range of length and time scales with modern computational resources. In this study, we develop a robust, efficient and high-order accurate numerical methods and techniques to tackle the challenges. First, we use high-order spatial discretization using (hybridized) discontinuous Galerkin (DG) methods. The DG method combines the advantages of finite volume and finite element methods. As such, it is well-suited to problems with large gradients including shocks and with complex geometries, and large-scale simulations. However, DG typically has many degrees-of-freedoms. To mitigate the expense, we use hybridized DG (HDG) method that introduces new “trace unknowns” on the mesh skeleton (mortar interfaces) to eliminate the local “volume unknowns” with static condensation procedure and reduces globally coupled system when implicit time-stepping is required. Also, since the information between the elements is exchanged through the mesh skeleton, the mortar interfaces can be used as a glue to couple multi-phase regions, e.g., solid and fluid regions, or non-matching grids, e.g., a rotating mesh and a stationary mesh. That is the HDG method provides an efficient and flexible coupling environment compared to standard DG methods. Second, we develop an HDG-DG IMEX scheme for an efficient time integrating scheme. The idea is to divide the governing equations into stiff and nonstiff parts, implicitly treat the former with HDG methods, and explicitly treat the latter with DG methods. The HDG-DG IMEX scheme facilitates high-order temporal and spatial solutions, avoiding too small a time step. Numerical results show that the HDG-DG IMEX scheme is comparable to an explicit Runge-Kutta DG scheme in terms of accuracy while allowing for much larger timestep sizes. We also numerically observe that IMEX HDG-DG scheme can be used as a tool to suppress the high-frequency modes such as acoustic waves or fast gravity waves in atmospheric or ocean models. In short, IMEX HDG-DG methods are attractive for applications in which a fast and stable solution is important while permitting inaccurate processing of the fast modes. Third, we also develop an EXPONENTIAL DG scheme for an efficient time integrators. Similar to the IMEX method, the governing equations are separated into linear and nonlinear parts, then the two parts are spatially discretized with DG methods. Next, we analytically integrate the linear term and approximate the nonlinear term with respect to time. This method accurately handles the fast wave modes in the linear operator. To efficiently evaluate a matrix exponential, we employ the cutting-edge adaptive Krylov subspace method. Finally, we develop a sliding-mesh interface by combining nonconforming treatment and the arbitrary Lagrangian-Eulerian (ALE) scheme for simulating rotating flows, which are important to estimate the characteristics of a rotating wind turbine or understanding vortical structures shown in atmospheric or astronomical phenomena. To integrate the rotating motion of the domain, we use the ALE formulation to map the governing equation to the stationary reference domain and introduce mortar interfaces between the stationary mesh and the rotating mesh. The mortar structure on the sliding interface changes dynamically as the mesh rotates

This book focuses on motions of incompressible ?uids of a freely moving surface being in?uenced by both the Earth’s rotation and density strati?cation. In contrast to traditional textbooks in the ?eld of geophysical ?uid dynamics, such as those by by Cushman-Roisin (1994) and Gill (1982), this book uses the method of proce- oriented hydrodynamic modelling to illustrate a rich variety of ?uid phenomena. To this end, the reader can adopt the model codes, found on the Springer server accompanying this book, to reproduce most graphs of this book and, even better, to create animation movies. The reader can also employ the codes as templates for own independent studies. This can be done by a lay person as a hobby activity, undergraduate or postgraduate students as part of their education, or professional scientists as part of research. Exercises of this book are run with open-source software that can be freely downloaded from the Internet. This includes the FORTRAN 95 compiler “G95” used for execution of model simulations, the data visualisation program “SciLab”, and “ImageMagick” for the creation of graphs and GIF animations, which can be watched with most Internet browsers.

The central theme of the book is the flow of information from experimental approaches in biofilm research to simulation and modeling of complex wastewater systems. Probably the greatest challenge in wastewater research lies in using the methods and the results obtained in one scientific discipline to design intelligent experiments in other disciplines, and eventually to improve the knowledge base the practitioner needs to run wastewater treatment plants. The purpose of Biofilms in Wastewater Treatment is to provide engineers with the knowledge needed to apply the new insights gained by researchers. The authors provide an authoritative insight into the function of biofilms on a technical and on a lab-scale, cover some of the exciting new basic microbiological and wastewater engineering research involving molecular biology techniques and microscopy, and discuss recent attempts to predict the development of biofilms. This book is divided into 3 sections: Modeling and Simulation; Architecture, Population Structure and Function; and From Fundamentals to Practical Application, which all start with a scientific question. Individual chapters attempt to answer the question and present different angles of looking at problems. In addition there is an extensive glossary to familiarize the non-expert with unfamiliar terminology used by microbiologists and computational scientists. The colour plate section of this book can be downloaded by clicking here. (PDF Format 1 MB)

Composite materials are used as substitutions of metals/traditional materials in aerospace, automotive, civil, mechanical and other industries. The present book collects the current knowledge and recent developments in the characterization and application of composite materials. To this purpose the volume describes the outstanding properties of this class of advanced material which recommend it for various industrial applications.

This book presents the technology of millimetre waves and Terahertz (THz) antennas. It highlights the importance of moderate and high-gain aperture antennas as key devices for establishing point-to-point and point-to-multipoint radio links for far-field and near-field applications, such as high data-rate communications, intelligent transport, security imaging, exploration and surveillance systems. The book provides a comprehensive overview of the key antenna technologies developed for the mm wave and THz domains, including established ones – such as integrated lens antennas, advanced 2D and 3D horn antennas, transmit and reflect arrays, and Fabry-Perot antennas – as well as emerging metasurface antennas for near-field and far-field applications. It describes the pros and cons of each antenna technology in comparison with other available solutions, a discussion supplemented by practical examples illustrating the step-by-step implementation procedures for each antenna type. The measurement techniques available at these frequency ranges are also presented to close the loop of the antenna development cycle. In closing, the book outlines future trends in various antenna technologies, paving the way for further developments. Presenting content originating from the five-year ESF research networking program ‘Newfocus’ and co-authored by the most active and highly cited research groups in the domain of mm- and sub-mm-wave antenna technologies, the book offers a valuable guide for researchers and engineers in both industry and academia.

This book gathers outstanding papers presented at the International Conference on Advances in Materials and Manufacturing Engineering (ICAMME 2019), held at KIIT Deemed to be University, Bhubaneswar, India, from 15 to 17 March 2019. It covers theoretical and empirical developments in various areas of mechanical engineering, including manufacturing, production, machine design, fluid/thermal engineering, and materials.

Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.