Ebook: Spectral Methods for Incompressible Viscous Flow

This book provides a comprehensive discussion of Fourier and Chebyshev spectral methods for the computation of incompressible viscous flows, based on the Navier-Stokes equations. The book is in three parts. The first part presents the fundamentals of the Fourier and Chebyshev methods for the solution of the Navier-Stokes equations considered in vorticity-streamfunction and velocity-pressure formulations. The third part of the book is concerned with the solution of stiff and singular problems, and with the domain decomposition method.
Every topic is accompanied by numerical examples, which further illustrate and assess the methods. Graduate students and researchers in applied mathematics and engineering working in fluid dxnamics, scientific computing, and numerical analysis will find this book of interest.

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This book provides a comprehensive discussion of Fourier and Chebyshev spectral methods for the computation of incompressible viscous flows, based on the Navier-Stokes equations. The book is in three parts. The first part presents the fundamentals of the Fourier and Chebyshev methods for the solution of the Navier-Stokes equations considered in vorticity-streamfunction and velocity-pressure formulations. The third part of the book is concerned with the solution of stiff and singular problems, and with the domain decomposition method.
Every topic is accompanied by numerical examples, which further illustrate and assess the methods. Graduate students and researchers in applied mathematics and engineering working in fluid dxnamics, scientific computing, and numerical analysis will find this book of interest.

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This book provides a comprehensive discussion of Fourier and Chebyshev spectral methods for the computation of incompressible viscous flows, based on the Navier-Stokes equations. The book is in three parts. The first part presents the fundamentals of the Fourier and Chebyshev methods for the solution of the Navier-Stokes equations considered in vorticity-streamfunction and velocity-pressure formulations. The third part of the book is concerned with the solution of stiff and singular problems, and with the domain decomposition method.
Every topic is accompanied by numerical examples, which further illustrate and assess the methods. Graduate students and researchers in applied mathematics and engineering working in fluid dxnamics, scientific computing, and numerical analysis will find this book of interest.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-6
Front Matter....Pages 7-7
Fundamentals of spectral methods....Pages 9-15
Fourier Method....Pages 17-37
Chebyshev method....Pages 39-100
Time-dependent equations....Pages 101-154
Front Matter....Pages 155-155
Navier-Stokes equations for incompressible fluids....Pages 157-166
Vorticity-Streamfunction Equations....Pages 167-206
Velocity-Pressure Equations....Pages 207-293
Front Matter....Pages 295-295
Stiff and singular problems....Pages 297-338
Domain Decomposition Method....Pages 339-388
Back Matter....Pages 389-434

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This book provides a comprehensive discussion of Fourier and Chebyshev spectral methods for the computation of incompressible viscous flows, based on the Navier-Stokes equations. The book is in three parts. The first part presents the fundamentals of the Fourier and Chebyshev methods for the solution of the Navier-Stokes equations considered in vorticity-streamfunction and velocity-pressure formulations. The third part of the book is concerned with the solution of stiff and singular problems, and with the domain decomposition method.
Every topic is accompanied by numerical examples, which further illustrate and assess the methods. Graduate students and researchers in applied mathematics and engineering working in fluid dxnamics, scientific computing, and numerical analysis will find this book of interest.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-6
Front Matter....Pages 7-7
Fundamentals of spectral methods....Pages 9-15
Fourier Method....Pages 17-37
Chebyshev method....Pages 39-100
Time-dependent equations....Pages 101-154
Front Matter....Pages 155-155
Navier-Stokes equations for incompressible fluids....Pages 157-166
Vorticity-Streamfunction Equations....Pages 167-206
Velocity-Pressure Equations....Pages 207-293
Front Matter....Pages 295-295
Stiff and singular problems....Pages 297-338
Domain Decomposition Method....Pages 339-388
Back Matter....Pages 389-434
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