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© 2011

Numerical Methods for Two-phase Incompressible Flows

Book

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 40)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Sven Gross, Arnold Reusken
    Pages 1-30
  3. One-phase incompressible flows

    1. Front Matter
      Pages 31-31
    2. Sven Gross, Arnold Reusken
      Pages 33-50
    3. Sven Gross, Arnold Reusken
      Pages 51-81
    4. Sven Gross, Arnold Reusken
      Pages 83-98
    5. Sven Gross, Arnold Reusken
      Pages 99-158
  4. Two-phase incompressible flows

    1. Front Matter
      Pages 159-159
    2. Sven Gross, Arnold Reusken
      Pages 161-195
    3. Sven Gross, Arnold Reusken
      Pages 197-281
    4. Sven Gross, Arnold Reusken
      Pages 283-295
    5. Sven Gross, Arnold Reusken
      Pages 297-323
  5. Mass transport

    1. Front Matter
      Pages 325-325
    2. Sven Gross, Arnold Reusken
      Pages 327-344
    3. Sven Gross, Arnold Reusken
      Pages 345-381
  6. Surfactant transport

    1. Front Matter
      Pages 383-383
    2. Sven Gross, Arnold Reusken
      Pages 385-390
    3. Sven Gross, Arnold Reusken
      Pages 391-430
  7. Appendix

    1. Front Matter
      Pages 431-431
    2. Sven Gross, Arnold Reusken
      Pages 433-438

About this book

Introduction

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.

Keywords

Navier-Stokes equations computational fluid dynamics finite element methods level set methods two-phase flows

Authors and affiliations

  1. 1., Institut für Numerische SimulationUniversität BonnBonnGermany
  2. 2.LS Numerische MathematikRWTH AachenAachenGermany

About the authors

Arnold Reusken is professor of Numerical Analysis at RWTH-Aachen. His research areas are: analysis and application of multigrid techniques, finite element methods, fast iterative methods for discretized PDEs, numerical methods for two-phase incompressible flow problems. 

Sven Gross is a PostDoc at the Hausdorff Center for Mathematics working at the Institute for Numerical Simulation at the University of Bonn. His research interests are adaptive extended finite element methods for two-phase incompressible flows and inverse problems in the context of chemical engineering applications. He is one of the core-developers of the two-phase flow solver DROPS.

Bibliographic information

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Reviews

From the reviews:

“This book is a first work providing an introduction to and an overview of such numerical methods. Some important and specific topics are considered in five parts of the book. … The material is intelligible to readers with a basic knowledge of numerical treatment of one-phase flow problems. … a basic book to researchers already working in the field of numerical simulation of two-phase flows.” (Titus Petrila, Zentralblatt MATH, Vol. 1222, 2011)

“This book gives a mathematically rigorous introduction to the application of finite element methods in the field of incompressible two-phase flows. … the authors not only present an extensive literature review and a number of established results, but also identify several knowledge gaps where few results are known for two-phase flows. … I find this book highly interesting. In particular, I strongly recommend it as preparatory reading for the Ph.D. students or young scientists in the field … .” (Tore Flåtten, Mathematical Reviews, January, 2013)