Characteristics Finite Element Methods in Computational Fluid Dynamics

✍ Scribed by Professor Dr. Joe Iannelli (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2006
• Tongue: English
• Leaves: 743
• Series: Computational Fluid and Solid Mechanics
• Edition: 1
• Category: Library

✦ Synopsis

This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. The fluid dynamics equations are derived from basic thermo-mechanical principles and the multi-dimensional and infinite-directional upstream procedure is developed by combining a finite element discretization of a characteristics-bias system with an implicit Runge-Kutta time integration. For the computational solution of the Euler and Navier Stokes equations, the procedure relies on the mathematics and physics of multi-dimensional characteristics. As a result, 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.

✦ Table of Contents

Front Matter....Pages I-XXV
Governing Equations of Fluid Mechanics....Pages 1-40
Constitutive and State Equations....Pages 41-49
State Equations for Reacting Air....Pages 51-92
Euler and Navier Stokes Systems....Pages 93-106
Quasi One-Dimensional and Free-Surface Equations....Pages 107-147
Overview of CFD Algorithm Development....Pages 149-165
The Finite Element Method....Pages 167-224
Non-Linearly Stable Implicit Runge-Kutta Time Integrations....Pages 225-240
One-Dimensional Non-Discrete Characteristics-Bias Resolution....Pages 241-264
Characteristics-Bias Controller and Length....Pages 265-277
Computational Analysis of Quasi-1-D Incompressible Flows....Pages 279-319
Numerical Study of Generalized Quasi-1-D Free Surface Flows....Pages 321-387
CFD Investigation of Generalized Quasi-1-D Compressible Flows....Pages 389-460
Multi-Dimensional Characteristics and Characteristics-Bias Systems....Pages 461-492
Multi-Dimensional Incompressible Flows....Pages 493-569
Multi-Dimensional Free-Surface Flows....Pages 571-634
Multi-Dimensional Compressible Flows....Pages 635-710
Back Matter....Pages 711-727

✦ Subjects

Engineering Fluid Dynamics;Computational Science and Engineering;Fluids;Numerical and Computational Methods in Engineering