Boundary and Interior Layers: Computational and Asymptotic Methods

By A. I. Bail

This book introduces boundary layer theory and its applications to real-world problems in engineering and the physical sciences. It provides a comprehensive overview of the subject, with a focus on the latest computational and asymptotic methods.

Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2024 (Lecture Notes in Computational Science and Engineering Book 108)

by Ashish Tewari

5 out of 5

Language	:	English
File size	:	9195 KB
Print length	:	322 pages
Screen Reader	:	Supported

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Boundary layer theory is a mathematical tool that is used to describe the behavior of fluids and gases near solid surfaces. It is used in a wide variety of applications, including the design of aircraft, ships, and cars, the analysis of chemical reactions, and the study of the atmosphere and oceans.

This book is divided into three parts. The first part provides an to boundary layer theory, including the basic equations, the different types of boundary layers, and the methods used to solve them. The second part of the book discusses computational methods for solving boundary layer problems. These methods include the finite difference method, the finite element method, and the spectral method.

The third part of the book focuses on asymptotic methods for solving boundary layer problems. These methods are based on the assumption that the boundary layer is thin compared to the overall flow field. They provide a powerful tool for obtaining approximate solutions to boundary layer problems.

This book is a valuable resource for researchers and students in applied mathematics, engineering, and physics. It is also a useful reference for engineers and scientists who use boundary layer theory in their work.

Table of Contents

• Boundary Layer Equations
• Types of Boundary Layers
• Computational Methods
• Finite Difference Method
• Finite Element Method
• Spectral Method
• Asymptotic Methods
• Method of Matched Asymptotic Expansions
• Applications
• References

Boundary layer theory is a mathematical tool that is used to describe the behavior of fluids and gases near solid surfaces. It is used in a wide variety of applications, including the design of aircraft, ships, and cars, the analysis of chemical reactions, and the study of the atmosphere and oceans.

The basic equations of boundary layer theory are the Navier-Stokes equations. These equations describe the conservation of mass, momentum, and energy in a fluid. However, the Navier-Stokes equations are nonlinear and difficult to solve. In Free Download to make them more manageable, boundary layer theory assumes that the boundary layer is thin compared to the overall flow field. This assumption allows us to simplify the Navier-Stokes equations and obtain approximate solutions to boundary layer problems.

Boundary Layer Equations

The boundary layer equations are a set of simplified Navier-Stokes equations that are used to describe the flow of fluids and gases near solid surfaces. The boundary layer equations are derived from the Navier-Stokes equations by assuming that the boundary layer is thin compared to the overall flow field.

The boundary layer equations consist of three equations: the continuity equation, the momentum equation, and the energy equation. The continuity equation states that the mass of fluid flowing into a control volume must equal the mass of fluid flowing out of the control volume. The momentum equation states that the momentum of fluid flowing into a control volume must equal the momentum of fluid flowing out of the control volume plus the forces acting on the fluid within the control volume. The energy equation states that the energy of fluid flowing into a control volume must equal the energy of fluid flowing out of the control volume plus the heat added to the fluid within the control volume.

The boundary layer equations can be solved using a variety of methods, including the finite difference method, the finite element method, and the spectral method. These methods are described in detail in the following sections.

Types of Boundary Layers

There are two main types of boundary layers: laminar boundary layers and turbulent boundary layers. Laminar boundary layers are characterized by smooth, Free Downloadly flow. Turbulent boundary layers are characterized by chaotic, disFree Downloaded flow.

Laminar boundary layers occur when the fluid is flowing at a low velocity. As the velocity of the fluid increases, the boundary layer becomes turbulent. The transition from laminar to turbulent flow occurs at a critical Reynolds number. The Reynolds number is a dimensionless number that characterizes the ratio of inertial forces to viscous forces.

The type of boundary layer that occurs in a particular application depends on the velocity of the fluid, the viscosity of the fluid, and the roughness of the surface.

Computational Methods

Computational methods are used to solve boundary layer problems. These methods include the finite difference method, the finite element method, and the spectral method.

The finite difference method is a numerical method that approximates the solution to a differential equation by replacing the derivatives with finite differences. The finite element method is a numerical method that approximates the solution to a differential equation by dividing the domain into a number of elements and solving the equation on each element. The spectral method is a numerical method that approximates the solution to a differential equation by expanding the solution in a series of basis functions.

The choice of computational method depends on the accuracy, efficiency, and ease of implementation required.

Finite Difference Method

The finite difference method is a numerical method that approximates the solution to a differential equation by replacing the derivatives with finite differences. The finite difference method is a simple and efficient method, but it can be inaccurate for problems with complex geometries.

Finite Element Method

The finite element method is a numerical method that approximates the solution to a differential equation by dividing the domain into a number of elements and solving the equation on each element. The finite element method is a more accurate method than the finite difference method, but it can be more computationally expensive.

Spectral Method

The spectral method is a numerical method that approximates the solution to a differential equation by expanding the solution in a series of basis functions. The spectral method is a very accurate method, but it can be computationally expensive.

Asymptotic Methods

Asymptotic methods are used to obtain approximate solutions to boundary layer problems. These methods are based on the assumption that the boundary layer is thin compared to the overall flow field. Asymptotic methods provide a powerful

Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2024 (Lecture Notes in Computational Science and Engineering Book 108)

by Ashish Tewari

5 out of 5

Language	:	English
File size	:	9195 KB
Print length	:	322 pages
Screen Reader	:	Supported

FREE