This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
This volume presents the emerging applications of immersed boundary (IB) methods in computational mechanics and complex CFD calculations. It discusses formulations of different IB implementations and also demonstrates applications of these methods in a wide range of problems. It will be of special value to researchers and engineers as well as graduate students working on immersed boundary methods, specifically on recent developments and applications. The book can also be used as a supplementary textbook in advanced courses in computational fluid dynamics.
This book provides an introduction to the immersed interface method (IIM), a powerful numerical method for solving interface problems and problems defined on irregular domains for which analytic solutions are rarely available. This book gives a complete description of the IIM, discusses recent progress in the area, and describes numerical methods for a number of classic interface problems. It also contains many numerical examples that can be used as benchmark problems for numerical methods designed for interface problems on irregular domains.
This IMA Volume in Mathematics and its Applications PARTICULATE FLOWS: PROCESSING AND RHEOLOGY is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Donald A. Drew, Daniel D. Joseph, and Stephen L. Passman for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Particulate Flows: Processing and Rheology was held January 8-12, 1996 at the Institute for Mathematics and its Applications on the University of Minnesota Twin Cities campus as part of the 1995- 96 Program on Mathematical Methods in Materials Science. There were about forty participants, and some lively discussions, in spite of the fact that bad weather on the east coast kept some participants from attending, and caused scheduling changes throughout the workshop. Heterogeneous materials can behave strangely, even in simple flow sit uations. For example, a mixture of solid particles in a liquid can exhibit behavior that seems solid-like or fluid-like, and attempting to measure the "viscosity" of such a mixture leads to contradictions and "unrepeatable" experiments. Even so, such materials are commonly used in manufacturing and processing.
“The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It is very original. There is no other book on this topic.” —René de Borst, Eindhoven University of Technology Written by leading experts in the field and featuring fully integrated colour throughout, Isogeometric Analysis provides a groundbreaking solution for the integration of CAD and FEA technologies. Tom Hughes and his researchers, Austin Cottrell and Yuri Bazilevs, present their pioneering isogeometric approach, which aims to integrate the two techniques of CAD and FEA using precise NURBS geometry in the FEA application. This technology offers the potential to revolutionise automobile, ship and airplane design and analysis by allowing models to be designed, tested and adjusted in one integrative stage. Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique. The authors offer a clear explanation as to how to add isogeometric capabilities to existing finite element computer programs, demonstrating how to implement and use the technology. Detailed programming examples and datasets are included to impart a thorough knowledge and understanding of the material. Provides examples of different applications, showing the reader how to implement isogeometric models Addresses readers on both sides of the CAD/FEA divide Describes Non-Uniform Rational B-Splines (NURBS) basis functions
The field of Large Eddy Simulations is reaching a level of maturity that brings this approach to the mainstream of engineering computations, while it opens opportunities and challenges. The main objective of this volume is to bring together leading experts in presenting the state-of-the-art and emerging approaches for treating complex effects in LES. A common theme throughout is the role of LES in the context of multiscale modeling and simulation.
This book gathers the proceedings of the 12th instalment in the bi-annual Workshop series on Direct and Large Eddy Simulation (DLES), which began in 1994 and focuses on modern techniques used to simulate turbulent flows based on the partial or full resolution of the instantaneous turbulent flow structure. With the rapidly expanding capacities of modern computers, this approach has attracted more and more interest over the years and will undoubtedly be further enhanced and applied in the future. Hybrid modelling techniques based on a combination of LES and RANS approaches also fall into this category and are covered as well. The goal of the Workshop was to share the state of the art in DNS, LES and related techniques for the computation and modelling of turbulent and transitional flows. The respective papers highlight the latest advances in the prediction, understanding and control of turbulent flows in academic and industrial applications.
An introduction to CFD fundamentals and using commercial CFD software to solve engineering problems, designed for the wide variety of engineering students new to CFD, and for practicing engineers learning CFD for the first time. Combining an appropriate level of mathematical background, worked examples, computer screen shots, and step by step processes, this book walks the reader through modeling and computing, as well as interpreting CFD results. The first book in the field aimed at CFD users rather than developers. New to this edition: A more comprehensive coverage of CFD techniques including discretisation via finite element and spectral element as well as finite difference and finite volume methods and multigrid method. Coverage of different approaches to CFD grid generation in order to closely match how CFD meshing is being used in industry. Additional coverage of high-pressure fluid dynamics and meshless approach to provide a broader overview of the application areas where CFD can be used. 20% new content .
This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.
This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.
