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Fluid Dynamics Part 2 Asymptotic Problems of Fluid Dynamics 1st Edition by Anatoly I Ruban ISBN 0199681740 9780199681747

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Fluid Dynamics Part 2 Asymptotic Problems of Fluid Dynamics 1st Edition Anatoly I. Ruban Digital Instant Download

Author(s): Anatoly I. Ruban
ISBN(s): 9780199681747, 0199681740
Edition: 1
File Details: PDF, 2.97 MB
Year: 2015
Language: english
SKU: EB-5892874 Category: Tag:

Fluid Dynamics Part 2 Asymptotic Problems of Fluid Dynamics 1st Edition by Anatoly I Ruban – Ebook PDF Instant Download/Delivery: 0199681740, 9780199681747
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ISBN 10: 0199681740 
ISBN 13: 9780199681747
Author: Anatoly I Ruban

This is the second volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. In Part 2 the reader is introduced to asymptotic methods, and their applications to fluid dynamics. Firstly, it discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The authors then consider supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. They also discuss the second order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are examined in detail. Part 2 concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered, the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stokes paradox. The authors show that this paradox can be resolved using the formalism of matched asymptotic expansions.

Fluid Dynamics Part 2 Asymptotic Problems of Fluid Dynamics 1st Table of contents:

1. Perturbation Methods
 1.1 Coordinate Asymptotic Expansions
  1.1.1 Taylor expansion
  1.1.2 Asymptotic expansion of an integral
  1.1.3 Basic definitions
  Exercises 1
 1.2 Laplace’s Method for Integrals
  1.2.1 Underlying idea
  1.2.2 Watson’s lemma
  1.2.3 Steepest descent method
  Exercises 2
 1.3 Parametric Expansions
  1.3.1 Regular perturbations
  1.3.2 Singular perturbations
 1.4 Method of Matched Asymptotic Expansions
  1.4.1 Formalism of the method
  1.4.2 Additional comments
  Exercises 3
 1.5 Method of Multiple Scales
  1.5.1 Solution with straightforward asymptotic expansions
  1.5.2 Exact solution
  1.5.3 Solution with the method of multiple scales
  Exercises 4
 1.6 The Method of Strained Coordinates
  1.6.1 Limit cycle of the Van der Pol oscillator
  1.6.2 Lighthill’s technique
  1.6.3 Renormalization method
  Exercises 5
 1.7 Adiabatic Invariance and the WKB Method
  1.7.1 Adiabatic invariance
  1.7.2 The WKB Method
  Exercises 6

2. Asymptotic Problems of Subsonic Flow Theory
 2.1 Thin Aerofoil in Incompressible Flow
  2.1.1 Linearized equations
  2.1.2 Boundary-value problem in complex plane
  2.1.3 Solution of Problem 2.1
  2.1.4 Lift force and pressure on aerofoil surface
  2.1.5 Sokhotsky–Plemelj’s formulae
  Exercises 7
 2.2 Thin Aerofoil in Subsonic Flow
  2.2.1 Linearized equations
  2.2.2 Prandtl–Glauert rules
  Exercises 8
 2.3 Separated Flow Past Thin Aerofoil
  2.3.1 Problem formulation
  2.3.2 Thin aerofoil approximation
  2.3.3 Solution of Problem 2.2
  Exercises 9
 2.4 Unsteady Flow Past Thin Aerofoil
  2.4.1 Wake behind the aerofoil
  2.4.2 Linearized equations
  2.4.3 Boundary-value problem in complex plane
  2.4.4 Oscillating aerofoil
  Exercises 10
 2.5 Large Aspect Ratio Wing

3. Supersonic Flows Past Thin Aerofoils
 3.1 Problem Formulation
  Exercises 11
 3.2 Linear Theory
  3.2.1 Shock conditions
  3.2.2 Flow behind the shock
  3.2.3 Ackeret formula
  Exercises 12
 3.3 Second-Order Approximation
  3.3.1 Governing equations
  3.3.2 Flow analysis in the inner region
  3.3.3 Solution of the quadratic problem
 3.4 Far-Field Behaviour
  3.4.1 Solution for the outer region
  3.4.2 Formation of the N-wave
  Exercises 13

4. Transonic Flows
 4.1 Governing Equations
 4.2 Far-Field Analysis
  4.2.1 Phase portrait
  4.2.2 Limiting characteristic
  4.2.3 Closing shock
  Exercises 14
 4.3 Kármán–Guderley Equation
  4.3.1 Numerical example
  4.3.2 Hodograph method
 4.4 Transonic Flow Separation at a Corner
  4.4.1 Flow analysis in physical variables
  4.4.2 Numerical results
  4.4.3 Analysis in the hodograph plane
 4.5 Transonic Prandtl–Meyer Flow
  4.5.1 Problem formulation
  4.5.2 Phase portrait
  4.5.3 Analysis in the hodograph plane
  Exercises 15

5. Hypersonic Flows
 5.1 Stabilization Principle
 5.2 Newton–Busemann Theory
  5.2.1 Von Mises variables
  5.2.2 Asymptotic analysis of the flow
  Exercises 16
 5.3 Hypersonic Flows Past Thin Bodies
  5.3.1 Weak interaction
  5.3.2 Moderate and strong interaction flow regimes
  5.3.3 Strong interaction. Self-similar solutions
  5.3.4 Blunt nose effect
  Exercises 17

6. Low-Reynold-Number Flows
 6.1 Flow Past a Sphere
  6.1.1 Low-Reynolds-number flow analysis
  Exercises 18
  6.1.2 Second-order approximation
  6.1.3 Oseen approximation
  Exercises 19
 6.2 Flow Past a Circular Cylinder
  6.2.1 Leading-order inner solution
  6.2.2 Oseen approximation
  Exercises 20

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Tags: Anatoly I Ruban, Fluid Dynamics, Asymptotic