The finite element method for fluid dynamics

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. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics. Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz. Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation.

Introduction to the equations of fluid dynamics and the finite element approximation -- Convection-dominated problems : finite element approximations to the convection-diffusion-reaction equation -- The characteristic-based split (CBS) algorithm : a general procedure for compressible and incompressible flow -- Incompressible Newtonian laminar flows -- Incompressible non-Newtonian flows -- Free surface and buoyancy driven flows -- Compressible high-speed gas flow -- Turbulent flows -- Generalized flow and heat transfer in porous media -- Shallow-water problems -- Long and medium waves -- Short waves -- Fluid-structure interaction -- Biofluid dynamics -- Computer implementation of the CBS algorithm.