Overview

A comprehensive and structured introduction to finite element methods for incompressible fluid dynamics, covering both spatial and temporal discretization, from the Stokes equations to the direct numerical simulation of the Navier-Stokes equations. This book provides a rigorous yet practical introduction to the finite element method applied to incompressible fluid mechanics. Designed for graduate engineering students, researchers, and industry professionals, it guides readers from the physical foundations of the Navier-Stokes equations to advanced numerical implementations. Combining mathematical clarity with a progressive pedagogical approach, the authors introduce key concepts in numerical linear algebra, discretization techniques, and time-dependent simulations, before moving toward multidimensional problems and real-world applications. Emphasis is placed on understanding algorithms and developing computational autonomy rather than relying on black-box software solutions. At the intersection of physics, applied mathematics, and computational science, this volume offers both a structured learning path and a valuable reference for anyone working with the numerical simulation of incompressible flows.

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9782889157563

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Mejdi Azaïez is a specialist in computational fluid mechanics and applied mathematics. He was previously a senior lecturer at Paul Sabatier University in Toulouse and is currently a full professor at the Bordeaux Institute of Technology. His research activities are primarily devoted to the numerical solution of the Navier-Stokes equations. Michel Deville is an emeritus professor at the École polytechnique fédérale de Lausanne (EPFL), where he taught computational fluid mechanics. He is a member of ONERA’s High Scientific Council. Ernest Mund was a visiting professor at the Université libre de Bruxelles, following a career in nuclear reactor physics and applied mathematics at the Belgian National Fund for Scientific Research and at the Université catholique de Louvain. He was granted emeritus status at both institutions in 2006.

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