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.

Joe Iannelli received a Diploma in Fluid Dynamics from the von Karman Institute for Fluid Dynamics, a summa cum laude MSc "Laurea" in Aeronautical Engineering from the University of Palermo, and his PhD in Engineering Science, with concentration in compressible-flow CFD, from the University of Tennessee. After investigating CFD algorithms for reactive flows at ICOMP, NASA Lewis, now Glenn, he has been a tenured Associate Professor of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee, and is now an Associate Professor ( Reader ) of Aeronautical Engineering at the City University of London, where he also serves as director of the historically first British Center for Aeronautics. A senior member of the American Institute of Aeronautics and Astronautics and the recipient of several awards, including an Exxon Professorship and an Alumni Association Outstanding Teaching Award, both from the University of Tennessee, he has researched CFD algorithms for over two decades, has authored numerous papers in Finite Element CFD and remains actively engaged in teaching and research in Propulsion and Engineering and Scientific Computing.