Finite Element Methods for Computational Fluid Dynamics: A Practical Guide - Softcover

Kuzmin, Dmitri; Hämäläinen, Jari

Softcover

ISBN 10: 1611973600 ISBN 13: 9781611973600

Publisher: Society for Industrial and Applied Mathematics, 2016

Synopsis

This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, 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.

Finite Element Methods for Computational Fluid Dynamics: A Practical Guide 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, and covers 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 problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.

Audience: The text is aimed at advanced undergraduate and graduate students in computational engineering. It may also be useful to physicists, computational scientists, and developers of numerical simulation software.

Contents: Chapter 1: Notation and Preliminaries; Chapter 2: Introduction to Numerical Methods for PDEs; Chapter 3: Equations of Fluid Dynamics and Heat Transfer; Chapter 4: The Basics of the Finite Element Method for the One-Dimensional Heat Equation; Chapter 5: The Galerkin Finite Element Method for Two-Dimensional Problems; Chapter 6: Stabilization Techniques in One Dimension; Chapter 7: Stabilization Techniques in Multidimensions; Chapter 8: Advanced Methods for Incompressible Flow Problems; Chapter 9: Further Reading

About this title

Book Description

This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. The text is aimed at advanced undergraduate and graduate students in computational engineering.

About the Author

Dmitri Kuzmin is a computational mathematician and professor at Dortmund University of Technology (TU Dortmund) in Germany. He has authored more than 80 publications and co-edited two editions of the book Flux-Corrected Transport: Principles, Algorithms, and Applications (Springer). Professor Kuzmin's research is focused on the design of high-resolution finite element schemes for computational fluid dynamics. His contributions to the field include a variety of flux and slope limiting techniques for enforcing positivity constraints and discrete maximum principles.

Jari Hämäläinen is Professor of Industrial Mathematics at Lappeenranta University of Technology (LUT) in Lappeenranta, Finland. After obtaining his doctoral degree in 1993, he worked a decade in industry until he was appointed as a professor in 2004. His major research interests are computational fluid dynamics (CFD) and CFD-based optimization in industrial applications. He has supervised 10 doctoral students (dissertations in 2007-2014), published more than 100 scientific papers, and has 12 patents. Professor Hämäläinen is a member of the executive committee of European Research Community on Flow, Turbulence and Combustion (ERCOFTAC).

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2016
• ISBN 10: 1611973600
• ISBN 13: 9781611973600
• Binding: Paperback
• Language: English
• Number of pages: 330