Numerical Methods for Two phase Incompressible Flows

Author: Sven Gross
Publisher: Springer Science & Business Media
ISBN: 9783642196867
Format: PDF, Mobi
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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
Publisher: Birkhäuser
ISBN: 3319566024
Format: PDF, Kindle
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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
Publisher: Springer
ISBN: 3319233157
Format: PDF, Kindle
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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.

Navier Stokes Equations in Planar Domains

Author: Matania Ben-Artzi
Publisher: World Scientific
ISBN: 1783263016
Format: PDF
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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

Frontiers in Numerical Analysis

Author: James Blowey
Publisher: Springer Science & Business Media
ISBN: 3642556922
Format: PDF
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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.

Computational Methods for Fluid Dynamics

Author: Joel H. Ferziger
Publisher: Springer Science & Business Media
ISBN: 3642560261
Format: PDF, Docs
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In its third revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers. The authors describe in detail the most often used techniques. Included are advanced techniques in computational fluid dynamics, such as direct and large-eddy simulation of turbulence. Moreover, a new section deals with grid quality and an extended description of discretization methods has also been included. Common roots and basic principles for many apparently different methods are explained. The book also contains a great deal of practical advice for code developers and users.

Numerical Solution of the Incompressible Navier Stokes Equations

Author: L. Quartapelle
Publisher: Springer Science & Business Media
ISBN: 9783764329358
Format: PDF, ePub, Docs
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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.