The Finite Element Method for Fluid Dynamics


  • P. Nithiarasu, Professor, College of Engineering, University of Wales, Swansea, UK

The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations.

The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on:

  • Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems.
  • Biofluid dynamics, covering flow throughout the human arterial system.

Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers.

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Mechanical, Aerospace, Automotive, Marine, Biomedical, Environmental and Civil Engineers, applied mathematicians and computer aided engineering software developers


Book information

  • Published: November 2013
  • ISBN: 978-1-85617-635-4


"...this is a book that you simply cannot afford to be without."--INTERNATIONAL JOURNAL OF NUMERICAL METHODS IN ENGINEERING (previous edition)

Table of Contents

1. Introduction to the equations of fluid dynamics and the finite element approximation2. Convection dominated problems - finite element approximations to the convection-diffusion-reaction equation3. The characteristic-based split (CBS) algorithm4. Incompressible Newtonian laminar flows5. Incompressible non-Newtonian flows6. Free surface and buoyancy driven flows7. Compressible high-speed gas flow8. Turbulent flows9. Flow through porous media10. Shallow water problems11. Long and medium waves12. Short waves13. Local conservation14. Fluid-structure interaction15. Biofluid dynamics16. Micro-scale fluid dynamics and molecular dynamics17. Computer implementation of the CBS algorithmAppendices