Mathematical Modeling Of Unsteady Inviscid Flows
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Mathematical Modeling of Unsteady Inviscid Flows
This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research. The tools covered in this book allow the reader to develop physics-based mathematical models for a variety of flows, including attached and separated flows past wings, fins, and blades of various shapes undergoing arbitrary motions. The book covers all of the ingredients of these models: the solution of potential flows about arbitrary body shapes in two- and three-dimensional contexts, with a particular focus on conformal mapping in the plane; the decomposition of the flow into contributions from ambient vorticity and body motion; generalized edge conditions, of which the Kutta condition is a special case; and the calculation of force and moment, with extensive treatments of added mass and the influence of fluid vorticity. The book also contains an extensive primer with all of the necessary mathematical tools. The concepts are demonstrated on several example problems, both classical and modern.
Analytical Methods in Differential Equations
Author: Sergey V. Meleshko
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2025-02-17
The book compiles papers presented at the International Conference 'Advances in Applications of Analytical Methods in Solving Differential Equations', held in honour of Academician Lev V. Ovsiannikov’s 105th birthday anniversary. This collection reflects his extensive contributions to the theory of differential equations, modelling, and the application of analytical methods. In addition to classical methods such as analytical integration of systems of equations and their applications in various fields of Science and Engineering, the book explores new areas of research. This includes the application of group analysis to novel mathematical models and nonlinear problems, particularly equations with nonlocal terms (symmetries of difference and differential equations, as well as fractional differential equations). One of the notable contributions in the book is the development of a Hamiltonian approach for delay differential equations, representing a novel area of research that has not been previously explored. The book is anticipated to appeal to a broad audience of experts in applied mathematics, fluid dynamics, and modelling, as well as to young scientists and graduate students interested in the analysis of nonlinear equations.
Two-Dimensional Separated Flows
Two-Dimensional Separated Flows provides a systematic presentation of the theory of separated flow around bodies. The main classes of aerodynamic problems of plane-parallel flow around bodies are described, and the steady aerodynamic, unsteady aerodynamic, and statistical characteristics of a trailing wake are determined. Numerical methods based on the synthesis of models for non-viscous incompressible flow and boundary layer, algorithms, examples, and systematic comparisons are presented. The book also includes numerical results for the problem of separated flow around fixed, oscillating, and rotating cylinders, in addition to results for separated flow around an aerofoil over a wide range of angles. Two-Dimensional Separated Flows will benefit researchers and students studying aerodynamics, aircraft dynamics, aeroelasticity, and the aerodynamics of building structures.