Finite Element Methods for Computational Fluid Dynamics: A Practical Guide

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. A comprehensive review of stabilization techniques for convection-dominated transport problems introduces the reader to streamline diffusion methods, Petrov–Galerkin approximations and Taylor–Galerkin schemes among other topics. Subsequent material includes Petrov–Galerkin stabilization, classical projection schemes, Schur complement solvers and the k-epsilon turbulence model for incompressible flow problems. Although the text is primarily 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. The book begins at a basic level and advances to numerical tools for increasingly difficult flow problems, with an emphasis on practical implementation, in order to be accessible to readers with diverse backgrounds and interests.

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).