High resolution upwind and centred methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Direct applicability of the methods include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. For this third edition the book was thoroughly revised and contains substantially more, and new material both in its fundamental as well as in its applied parts.
Author(s): Toro E.F.
Edition: Third edition
Year: 2009
Language: English
Pages: 724
Summary of Numerical Aspects......Page 22
Explosions and Implosions......Page 23
Potential Applications......Page 24
The Numerical Flux......Page 25
The Numerical Source......Page 26
Reconstruction......Page 27
Current Research Topics......Page 28
A Method of Solution......Page 32
The Numerical Flux......Page 34
Long--Time Advection of Smooth Profiles......Page 36
Analysis in Multiple Space Dimensions......Page 38
Convergence Rates......Page 39
Concluding Remarks......Page 40
A Flux Limiter Centred (flic) Scheme......Page 41
Linear Advection with a Source Term......Page 42
Formulation of the Equations and Primitive Schemes......Page 44
Concluding Remarks......Page 46
Other Solvers......Page 48
Schemes for Two--Dimensional Nonlinear Systems......Page 49
Concluding Remarks......Page 50
Schemes for Three--Dimensional Nonlinear Systems......Page 52
General Domains and Coordinate Transformation......Page 54
Monotone Schemes and Godunov's Theorem......Page 56
Incompressible Viscous Flow......Page 59
Total Variation Diminishing ( TVD) Methods......Page 60
Numerical Flux and Numerical Source......Page 30
The Intercell Flux and the tvd Condition......Page 31
The Scheme......Page 33
Non--Linear Equation with a Source Term......Page 43
Remarks on Path Orderings......Page 47
Data Compatibility......Page 58
Elementary--Wave Solutions of the Riemann Problem......Page 64
The NUMERICA Library......Page 29
Adaptive Primitive--Conservative Schemes......Page 51
FORTRAN Program for Godunov's Method......Page 55
Introduction......Page 53
Summary......Page 35
Summary: Numerical Flux and Numerical Source......Page 37
The Burgers Equation with a Source Term......Page 45
The Finite Volume Method for Non--Cartesian Domains......Page 57
The Total Variation......Page 61
TVD and Monotonicity Preserving Schemes......Page 62
TVD Version of the waf Method......Page 65
The General Flux--Limiter Approach......Page 73
TVD Upwind Flux Limiter Schemes......Page 78
TVD Centred Flux Limiter Schemes......Page 83
TVD Conditions......Page 89
Construction of TVD Slopes......Page 90
Slope Limiters......Page 91
Limited Slopes Obtained from Flux Limiters......Page 93
TVD Schemes in the Presence of Diffusion Terms......Page 95
Numerical Results for Linear Advection......Page 96
