numerical methods for two phase incompressible flows 40 springer series in computational mathematics

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Numerical Methods For Two Phase Incompressible Flows

Author : Sven Gross
ISBN : 3642196861
Genre : Mathematics
File Size : 23. 52 MB
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This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.

Transport Processes At Fluidic Interfaces

Author : Dieter Bothe
ISBN : 9783319566023
Genre : Mathematics
File Size : 55. 30 MB
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There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface. This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”

Isogeometric Analysis And Applications 2014

Author : Bert Jüttler
ISBN : 9783319233154
Genre : Mathematics
File Size : 37. 94 MB
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Isogeometric Analysis is a groundbreaking computational approach that promises the possibility of integrating the finite element method into conventional spline-based CAD design tools. It thus bridges the gap between numerical analysis and geometry, and moreover it allows to tackle new cutting edge applications at the frontiers of research in science and engineering. This proceedings volume contains a selection of outstanding research papers presented at the second International Workshop on Isogeometric Analysis and Applications, held at Annweiler, Germany, in April 2014.

Frontiers In Numerical Analysis

Author : James Blowey
ISBN : 9783642556920
Genre : Mathematics
File Size : 82. 90 MB
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A set of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area. Detailed proofs of key results are provided. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians.

Navier Stokes Equations In Planar Domains

Author : Matania Ben-Artzi
ISBN : 9781783263011
Genre : Mathematics
File Size : 76. 98 MB
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This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”. A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem. This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics. Contents:Basic Theory:IntroductionExistence and Uniqueness of Smooth SolutionsEstimates for Smooth SolutionsExtension of the Solution OperatorMeasures as Initial DataAsymptotic Behavior for Large TimeSome Theorems from Functional AnalysisApproximate Solutions:IntroductionNotationFinite Difference Approximation to Second-Order Boundary-Value ProblemsFrom Hermitian Derivative to the Compact Discrete Biharmonic OperatorPolynomial Approach to the Discrete Biharmonic OperatorCompact Approximation of the Navier–Stokes Equations in Streamfunction FormulationFully Discrete Approximation of the Navier–Stokes EquationsNumerical Simulations of the Driven Cavity Problem Readership: Graduate students and researchers in applied mathematics (particularly computational fluid dynamics), partial differential equations, and mathematical physics (specifically nonlinear evolution equations). Key Features:Provides an up-to-date account of recent developments in vorticity theoryPresents comprehensive treatment of viscous flow problems in flat domainsAddresses the classical problem: How rapidly do rotating flows evolve in time?Includes theoretical and numerical methodsPresents state-of-the-art streamfunction formalism (theoretical and numerical)Keywords:Vorticity;Classical Energy Method;Leray;Asymptotic Behavior;Nonlinear System;Streamfunction Formulation;Steady States;Convergence Theorem;Periodic Solutions;FFT;Navier-Stokes Equations;Planar Domains;Compact Schemes;Streamfunction;Viscous FlowReviews:“It is well positioned as a reference for both theoretical and applied mathematicians, as well as a book that can be used by graduate students pursuing studies in mathematics, mathematical physics and fluid dynamics.”Zentralblatt MATH

Level Set Methods And Dynamic Implicit Surfaces

Author : Stanley Osher
ISBN : 9780387227467
Genre : Mathematics
File Size : 76. 76 MB
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Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area

Essential Computational Fluid Dynamics

Author : Oleg Zikanov
ISBN : 9781118174395
Genre : Science
File Size : 76. 11 MB
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This book serves as a complete and self-contained introduction to the principles of Computational Fluid Dynamic (CFD) analysis. It is deliberately short (at approximately 300 pages) and can be used as a text for the first part of the course of applied CFD followed by a software tutorial. The main objectives of this non-traditional format are: 1) To introduce and explain, using simple examples where possible, the principles and methods of CFD analysis and to demystify the `black box’ of a CFD software tool, and 2) To provide a basic understanding of how CFD problems are set and which factors affect the success and failure of the analysis. Included in the text are the mathematical and physical foundations of CFD, formulation of CFD problems, basic principles of numerical approximation (grids, consistency, convergence, stability, and order of approximation, etc), methods of discretization with focus on finite difference and finite volume techniques, methods of solution of transient and steady state problems, commonly used numerical methods for heat transfer and fluid flows, plus a brief introduction into turbulence modeling.

Turbulence And Interactions

Author : Michel O. Deville
ISBN : 9783662434895
Genre : Science
File Size : 68. 67 MB
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The book presents a snapshot of the state-of-art in the field of turbulence modeling and covers the latest developments concerning direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and other related topics. It provides readers with a comprehensive review of both theory and applications, describing in detail the authors’ own experimental results. The book is based on the proceedings of the third Turbulence and Interactions Conference (TI 2012), which was held on June 11-14 in La Saline-les-Bains, La Réunion, France and includes both keynote lectures and outstanding contributed papers presented at the conference. This multifaceted collection, which reflects the conference ́s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a practice-oriented guide for students, researchers and professionals in the field of computational fluid dynamics, turbulence modeling and related areas.

Finite Element Methods For Incompressible Flow Problems

Author : Volker John
ISBN : 9783319457505
Genre : Mathematics
File Size : 66. 93 MB
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This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

Numerical Methods For Nonlinear Partial Differential Equations

Author : Sören Bartels
ISBN : 9783319137971
Genre : Mathematics
File Size : 56. 46 MB
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The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

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