ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics

:	Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, Thomas A. Zang
:	Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics
:	Springer-Verlag
:	9783540307280
:	1
:	CHF 85.20
:

:	Analysis
:	English

:	596
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Following up the seminalSpectral Methods in Fluid Dynamics,Spectra Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting.

This book is a companion toSpectral Methods: Fundamentals in Single Domains.

	Preface	5
	Contents	9
	List of Figures	17
	List of Tables	22
	Contents of the Companion Book Spectral Methods – Fundamentals in Single Domains	23
	1. Fundamentals of Fluid Dynamics	29
	1.1 Introduction	29
	1.2 Fluid Dynamics Background	29
	1.3 Compressible Fluid Dynamics Equations	35
	1.4 Incompressible Fluid Dynamics Equations	49
	1.5 Linear Stability of Parallel Flows	55
	1.6 Stability Equations for Nonparallel Flows	64
	2. Single-Domain Algorithms and Applications for Stability Analysis	67
	2.1 Introduction	67
	2.2 Boundary-Layer Flows	69
	2.3 Linear Stability of Incompressible Parallel Flows	80
	2.4 Linear Stability of Compressible Parallel Flows	92
	2.5 Nonparallel Linear Stability	97
	2.6 Transient Growth Analysis	100
	2.7 Nonlinear Stability	103
	3. Single-Domain Algorithms and Applications for Incompressible Flows	111
	3.1 Introduction	111
	3.2 Conservation Properties and Time-Discretization	114
	3.3 Homogeneous Flows	126
	3.4 Flows with One Inhomogeneous Direction	149
	3.5 Flows with Multiple Inhomogeneous Directions	175
	3.6 Outflow Boundary Conditions	187
	3.7 Analysis of Spectral Methods for Incompressible Flows	190
	4. Single-Domain Algorithms and Applications for Compressible Flows	214
	4.1 Introduction	214
	4.2 Boundary Treatment for Hyperbolic Systems	214
	4.3 Boundary Treatment for the Euler Equations	230
	4.4 High-Frequency Control	235
	4.5 Homogeneous Turbulence	238
	4.6 Smooth, Inhomogeneous Flows	245
	4.7 Shock Fitting	253
	4.8 Shock Capturing	260
	5. Discretization Strategies for Spectral Methods in Complex Domains	263
	5.1 Introduction	263
	5.2 The Spectral Element Method (SEM) in 1D	265
	5.3 SEM for Multidimensional Problems	271
	5.4 Analysis of SEM and SEM-NI Approximations	283
	5.5 Some Numerical Results for the SEM- NI Approximations	299
	5.6 SEM for Stokes and Navier–Stokes Equations	304
	5.7 The Mortar Element Method (MEM)	315
	5.8 The Spectral Discontinuous Galerkin Method ( SDGM) in 1D	326
	5.9 SDGM for Multidimensional Problems	342
	5.10 SDGM for Diffusion Equations	349
	5.11 Analysis of SDGM	352
	5.12 SDGM for Euler and Navier–Stokes Equations	358
	5.13 The Patching Method	365
	5.14 3D Applications in Complex Geometries	378
	6. Solution Strategies for Spectral Methods in Complex Domains	384
	6.1 Introduction	384
	6.2 On Domain Decomposition Preconditioners	384
	6.3 (Overlapping) Schwarz Alternating Methods	389
	6.4 Schur Complement Iterative Methods	410
	6.5 Solution Algorithms for Patching Collocation Methods	427
	7. General Algorithms for Incompressible Navier– Stokes Equations	432
	7.1 Introduction	432
	7.2 High-Order Fractional-Step Methods	434
	7.3 Solution of the Algebraic System Associated with the Generalized Stokes Problem	440
	7.4 Algebraic Factorization Methods	450
	8. Spectral Methods Primer	459
	8.1 The Fourier System	459
	8.2 General Jacobi Polynomials in the Interval (- 1, 1)	469
	8.3 Chebyshev Polynomials	475
	8.4 Legendre Polynomials	479
	8.5 Modal and Nodal Boundary-Adapted Bases on the Interval	482
	8.6 Orthogonal Systems in Unbounded Domains	484
	8.7 Multidimensional Expansions	486
	8.8 Mappings	492
	8.9 Basic Spectral Discretization Methods	502
	Appendix A. Basic Mathematical Concepts	512
	A.1 Hilbert and Banach Spaces	512
	A.2 The Cauchy-Schwarz Inequality	514
	A.3 The Lax-Milgram Theorem	515
	A.4 Dense Subspace of a Normed Space	515
	A.5 The Spaces Cm(O), m = 0	516
	A.6 The Spaces Lp(O), 1 = p = +8	516
	A.7 Infinitely Differentiable Functions and Distributions	517
	A.8 Sobolev Spaces and Sobolev Norms	519
	A.9 The Sobolev Inequality	524
	A.10 The Poincar´ e Inequality	524
	Appendix B. Fast Fourier Transforms	525
	Appendix C. Iterative Methods for Linear Systems	531
	C.1 A Gentle Approach to Iterative Methods	531
	C.2 Descent Methods for Symmetric Problems	535
	C.3 Krylov Methods for Nonsymmetric Problems	540
	Appendix D. Time Discretizations	547
	D.1 Notation and Stability Definitions	547
	D.2 Standard ODE Methods	550
	D.3 Low-Storage Schemes	557
	Appendix E. Supplementary Material	559
	E.1 Numerical Solution of the Generalized Eigenvalue Problem	559
	E.2 Tau Correction for the Kleiser–Schumann Method	561
	E.3 The Piola Transform	563
	References	566
	Index	607