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Numerical methods for two-phase incompressible flows. (English) Zbl 1222.76002

Springer Series in Computational Mathematics 40. Berlin: Springer (ISBN 978-3-642-19685-0/hbk; 978-3-642-19686-7/ebook). xvii, 480 p. (2011).
There is an extensive literature on numerical methods for one-phase incompressible Navier-Stokes equations. Open source and commercial software packages are available and perform satisfactorily for a large class of such problems. In recent years, the numerical simulation of two-phase flows, in which two immiscible fluids with different physical properties are separated by an interface, is a topic of growing interest in computational fluid dynamics. The motion of these flows is governed by incompressible Navier-Stokes equations combined with coupling conditions at the interface.
Several difficulties, which are absent in one-phase flows, arise when solving the two-phase flow problems. As a consequence, numerical algorithms developed for one-phase flows cannot be directly applied to the simulation of two-phase flow problems. Until now, there are only few papers that address rigorous mathematical analysis of methods for two-phase flow problems. 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. Numerical treatment of the unknown interface is a difficult task even in the simplest cases, and numerical approximation of surface tension forces is often of major importance for a successful simulation. Simulation of mass and heat transport from one phase into other is also a difficult problem because the concentration of species is discontinuous across the interface. The simulation of surfactants, which are transported on the interface, is governed by the convection-diffusion equation on the interface only.
The book gives a complete treatment of the above problems in the sense that the models are derived, weak formulations are discussed, the discretization methods are introduced and analyzed, some iterative solvers are developed, and, finally, implementation aspects and results of numerical experiments are presented. Most of the methods treated in the book can be implemented in the open-access software package DROPS, and all numerical experiments given in the book were performed with this package. Of course, many interesting issues such as the modeling of evaporation, phase transition, topological singularities or reactions at interface cannot be treated in this introductory work. Instead, only incompressible flows are considered and, concerning the numerical methods, only finite element discretizations are treated.
The text aims at MSc and PhD students with specialization in numerical analysis or computational engineering. The material is intelligible to readers with a basic knowledge of numerical treatment of one-phase flow problems. The reviewer also recommends “Numerical methods for two-phase incompressible flows” as a basic book to researchers already working in the field of numerical simulation of two-phase flows.

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D45 Capillarity (surface tension) for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)

Software:

DROPS; NewtonLib; UG
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