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.

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."

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.

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."

Dieses Lehrbuch vermittelt die Wirkungsweise vieler unterschiedlicher Grundbausteine numerischer Algorithmen. UEbergeordnete Zielsetzung ist die Starkung der Fahigkeit, numerische Ergebnisse einschatzen und bewerten zu koennen, sowie die numerischen Werkzeuge auch in komplexeren Anwendungsszenarien flexibel und sachgemass kombinieren und anpassen zu koennen. Besonderer Wert wird dabei von Anfang an auf ein solides Verstandnis der Konzepte Kondition (eines Problems) und Stabilitat (eines Loesungsverfahrens) gelegt. Aufgrund der Vielzahl der in der Praxis benoetigten numerischen Bausteine wird eine methodenorientierte Einfuhrung zu den relevanten Themenschwerpunkten angeboten: Direkte und iterative Verfahren zur Loesung von Gleichungssystemen, Ausgleichsrechnung, Singularwertzerlegung, Eigenwertberechnung, Interpolation, schnelle Fouriertransformation, numerische Integration sowie numerische Verfahren fur gewoehnliche Differentialgleichungen. Zahlreiche illustrierende Beispiele vermitteln den konkreten Ablauf von Verfahren und verdeutlichen neue Konzepte, abschliessende UEbungsaufgaben runden die Kapitel ab. Die Inhalte selbst sind - soweit moeglich - so gestaffelt, dass den "Pflichtinhalten" optionale Vertiefungen folgen, in denen konzeptionelle Gesichtspunkte, ubergreifende Zusammenhange sowie rigorose Begrundungen starker betont werden. Das Buch eignet sich daher sowohl als Grundlage einer einsemestrigen einfuhrenden als auch einer weiterfuhrenden Numerik-Vorlesung im Ingenieurstudium, bietet aber auch die konzeptionellen Grundlagen fur die Numerikausbildung im Mathematikstudium.Die Autoren stellen auf Ihrer Webseite zusatzlich Vorlesungsfolien fur Dozenten, Multiple-Choice-Aufgaben sowie Matlabdemos bereit.Fur die 3. Auflage wurde das Buch vollstandig uberarbeitet und noch besser strukturiert.