Numerical Methods for Two-phase Incompressible Flows

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.

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

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)

• , Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

  Sven Gross

• LS Numerische Mathematik, RWTH Aachen, Aachen, Germany

  Arnold Reusken

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.

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