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Recent advances in scientific computing have caused the field of aerodynamics to change at a rapid pace, simplifying the design cycle of aerospace vehicles enormously – this book takes the readers from core concepts of aerodynamics to recent research, using studies and real-life scenarios to explain problems and their solutions. This book presents in detail the important concepts in computational aerodynamics and aeroacoustics taking readers from the fundamentals of fluid flow and aerodynamics to a more in-depth analysis of acoustic waves, aeroacoustics, computational modelling and processing. This book will be of use to students in multiple branches of engineering, physics and applied mathematics. Additionally, the book can also be used as a text in professional development courses for industry engineers and as a self-help reference for active researchers in both academia and the industry.

### Chapter 1. Elements of Continuum Mechanics for Fluid Flow and General Stress–Strain System

Abstract
The fundamental physical laws in fluid flows are obtained from the conservation of mass, translational momentum, and energy, with the latter being nothing but the first law of thermodynamics applied to a control volume system. While for solids and liquids, the properties vary continuously in their macroscopic states, it is not so apparent for gases, which is characterized by mobility at the molecular level. One describes the flow of gases from the average behavior of the molecular ensemble in the control volume. This approach presupposes the existence of very many large number of molecules in the control volume, so that the statistical description is feasible. This is the essence of the continuum assumption that despite the presence of discrete molecules constituting the system, one can approximate the assembly by continuous variation of macroscopic properties. Continuous variation of properties arises due to momentum and energy exchanges by incessant collisions of molecules taking place. One of the most relevant non-dimensional numbers, determining whether a gaseous flow can be considered continuum or one must use statistical approaches, is the Knudsen number.
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 2. Elementary Aerodynamics

Abstract
In Chap. 1, we have laid down the governing equations at different hierarchy levels, starting from the Navier–Stokes equation without the limiting Stokes’ hypothesis down to the inviscid, irrotational flow modeled by Laplace’s equation for velocity potential ($$\phi$$) and stream function ($$\psi$$) for 2D flows
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 3. Governing Equations for Aerodynamics and Acoustics

Abstract
Fluid dynamical governing equations are given by the conservation principles of mass, momentum, and energy as noted in Chap. 1. Although the Navier–Stokes equation is an application of Newton’s second law for fluid flows, one also assumes the relation between the stress and the rate of strain tensor. There are many versions of Navier–Stokes equation (NSE), depending upon the constitutive relation of the fluid medium. In the following, we will focus mainly on what is known as Newtonian fluid, for which the stress and rate of strain have linear relation.
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 4. Computational Incompressible Aerodynamics

Abstract
Analysis of aerodynamic properties of aerospace vehicles has now matured to a stage, where high accuracy computing can, to a large extent, replace the design data book’s sectional properties. In this chapter, we focus on main issues which make computational aerodynamics a practical tool.
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 5. Computational Compressible Aerodynamics

Abstract
In the previous chapter, we kept our attention focused on incompressible flow problems in aerodynamics for low and high Reynolds numbers.
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 6. Acoustic Wave Equation

Abstract
An acoustic signal or an acoustic disturbance consists of pressure oscillations traveling in an elastic medium. The variation of pressure can either be triggered by a vibrating surface (for example, diaphragm of a speaker) or by a turbulent fluid flow. In a broad sense, a sound wave is any disturbance that propagates in an elastic medium, which may be either a gas, a liquid, or a solid.
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 7. Solutions of Computational Acoustic Problems Using DRP Schemes

Abstract
Computational acoustics is an important and active research area [12, 13, 45, 47, 49]. Acoustic signals propagate in the form of longitudinal waves in air. Pressure fluctuations associated with acoustic signals are usually very small compared to the large background pressure field. The atmospheric pressure is around $$10^{5}$$ Pa, while the amplitude of the smallest recognizable acoustic disturbance for a human being is around $$10^{-5}$$ Pa.
Tapan K. Sengupta, Yogesh G. Bhumkar

### Chapter 8. Methodologies and Solutions of Computational Aeroacoustic Problems

Abstract
Computational aeroacoustics (CAA) is an important research area which connects aerodynamics and acoustics. This research area involves simulations of flow-induced acoustic noise and can be broadly categorized into three different methodologies based on the approach used for estimating acoustic field. First two methodologies use computed fluid flow information to further calculate acoustic field details using either an acoustic analogy approach or by solving set of perturbation equations.
Tapan K. Sengupta, Yogesh G. Bhumkar