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Finite element methods for computational fluid dynamics. A practical guide. (English) Zbl 1317.76001
Computational Science & Engineering 14. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-360-0/pbk). viii, 313 p. (2015).
This informal introduction to computational fluid dynamics and practical guide for numerical simulation of transport phenomena covers the derivation of the governing equations, the construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory. The book explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov-Galerkin approximations, Taylor-Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes. The book covers also the Petrov-Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the \(k\)-epsilon turbulence model in its presentation of the FEM for incompressible flow problems. Additionally, the book describes the open-source finite element library ELMER, which is recommended as a software development tool for advanced applications in an online component.

76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics