Author | Peyret, Roger. author |
---|---|

Title | Spectral Methods for Incompressible Viscous Flow [electronic resource] / by Roger Peyret |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2002 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-6557-1 |

Descript | XII, 434 p. online resource |

SUMMARY

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

I Basic spectral methods -- 1 Fundamentals of spectral methods -- 2 Fourier Method -- 3 Chebyshev method -- 4 Time-dependent equations -- II. Navier-Stokes equations -- 5 Navier-Stokes equations for incompressible fluids -- 6 Vorticity-Streamfunction Equations -- 7 Velocity-Pressure Equations -- III Special topics -- 8 Stiff and singular problems -- 9 Domain Decomposition Method -- Appendix A Formulas on Chebyshev polynomials -- A.1 Definition and general properties -- A.2 Differentiation -- A.3 Collocation points -- A.4 Truncated series expansion -- A.5 Lagrange interpolation polynomial -- A.6 Derivatives at Gauss-Lobatto points -- A.7 Integration -- A.8 Numerical integration based on Gauss-Lobatto points -- Appendix B Solution of a quasi-tridiagonal system -- Appendix C Theorems on the zeros of a polynomial -- References

Mathematics
Numerical analysis
Fluids
Fluid mechanics
Mathematics
Numerical Analysis
Fluid- and Aerodynamics
Engineering Fluid Dynamics