Theoretical and Computational Fluid Mechanics

Existence, Blowup and Discrete Exterior Calculus Problems, Volume II
1. Auflage 2025
ISBN: 978-1-032-98931-0
Verlag: Taylor & Francis Ltd

Buch, Englisch, 536 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Theoretical and Computational Fluid Mechanics: Existence, Blowup and Discrete Exterior Calculus Problems, Volume II is self-contained, though it builds upon the work of the previous volume in providing a comprehensive introduction to the mathematical theory of incompressible flows, with a focus on the foundational structures, analytical techniques, and open problems as-sociated with the Navier-Stokes equations. In this volume, emphasis is placed on the interplay between geometry, functional analysis, and partial differential equations that underpins much of modern fluid theory.

As a reference or teaching supplement, the book is accessible to anyone with a basic level of understanding of fluid dynamics and yet still engaging for those of a deeper understanding. The book is aimed at theorists and applied mathematicians from a wide range of scientific fields, including the social, health, and physical sciences. It provides a step-by-step guide to the construction of solutions of both elementary and open problems of viscous and non-viscous models, and for the applications of such models for the functional analysis and real analysis of data.

Features

· Offers a self-contained treatment that does not require a previous background in fluid dynamics

· Suitable as a reference text for graduate students, researchers, and professionals, and could easily be used as a teaching resource

· Provides various examples using Maple, Mathematica, and to a lesser extent MATLAB programming languages.

Zielgruppe

Postgraduate

Autoren/Hrsg.

Afas, Keith

Moschandreou, Terry E.

Nguyen, Khoa

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Ch 1 More on Euler’s Equations, Gas Dynamics and Boundary Layers Ch 2 Fixed Point Theory Ch 3 PNS: Existence of a Non-Cauchy sequence sending blowup points to infinity Ch 4 PNS-Relation between two-point and three-point correlation functions Ch 5 RANS and Turbulence Ch 6 The Cauchy Problem for the Abstract Navier Stokes Equations and Harmonic Analysis Tools Ch 7 Introduction to No finite time singularities for PNS Ch 8 Existence of solutions to 3D Periodic Navier-Stokes equations(PNS) Ch 9 Technical Heat transfer
and thermodynamics Concepts Ch 10 Introduction to Pulses, Waves and Locally Compact Spaces Ch 11 Helmholtz-Kelvin- Stokes Types of Invariants by Integration of Total Rotational Momentum Densities for Incompressible Flows and the Solution of the fourth Millennium Problem Ch 12 Application of Discrete Exterior Calculus to Fluid Mechanics Problems Ch A Computer Programs Index

Über Autor(innen)

Terry E. Moschandreou has taught mathematics at the University of Western Ontario in the School of Mathematical and Statistical Sciences where he worked for several years. He received his PhD degree in Applied Mathematics from the University of Western Ontario in 1996.

Keith Afas is a graduate researcher at the University of Western Ontario (UWO), who has been engaged in applied mathematics and
mathematical modelling research since 2014, leading to multiple first-author and co-author publications, posters, conference presentations, and book chapters in a variety of topics.

Khoa Nguyen has taught applied mathematics at Western University at London, Ontario, Canada since 2001 to present. Most
of his students are engineering and science students. His interests are varying from physics to engineering, mathematics, and applications of mathematics to these fields. He has had two publications on Physical Review D with his collaborators and a book on numerical methods in C and Matlab with his colleague. He has a wife and two sons. They live in London, Ontario, Canada.