Characteristics Finite Element Methods in Computational Fluid Dynamics

By: Giuseppe Iannelli, Joe Iannelli

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Hardcover | 22 August 2006

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756 Pages

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23.5 x 15.88 x 4.45

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This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. Several sections derive the Fluid Dynamics equations from thermo-mechanics principles and develop this multi-dimensional and infinite-directional upstream procedure by combining a finite element discretization with an implicit non-linearly stable Runge-Kutta time integration for the numerical solution of the Euler and Navier Stokes equations. Based on the mathematics and physics of multi-dimensional characteristics, convection as well as acoustics, and inducing by design a controllable multi-dimensional upwind bias that can be locally optimized, the procedure crisply captures contact discontinuities, normal as well as oblique shocks, and generates essentially non-oscillatory solutions for incompressible, subsonic, transonic, supersonic, and hypersonic inviscid and viscous flows with chemical reactions and work, heat and mass transfer.

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Paperback

Published: 12th February 2010

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A brief history of theoretical and computational fluid dynamics
Governing equations of fluid mechanics	p. 1
Constitutive and state equations	p. 41
State equations for reacting air	p. 51
Euler and Navier Stokes systems	p. 93
Quasi one-dimensional and free-surface equations	p. 107
Overview of CFD algorithm development	p. 149
The finite element method	p. 167
Non-linearly stable implicit Runge-Kutta time integrations	p. 225
One-dimensional non-discrete characteristics-bias resolution	p. 241
Characteristics-bias controller and length	p. 265
Computational analysis of quasi-1-D incompressible flows	p. 279
Numerical study of generalized quasi-1-D free surface flows	p. 321
CFD investigation of generalized quasi-1-D compressible flows	p. 389
Multi-dimensional characteristics and characteristics-bias systems	p. 461
Multi-dimensional incompressible flows	p. 493
Multi-dimensional free-surface flows	p. 571
Multi-dimensional compressible flows	p. 635
Table of Contents provided by Blackwell. All Rights Reserved.

Characteristics Finite Element Methods in Computational Fluid Dynamics

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