Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Third Edition

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. 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 This textbook gives a comprehensive and practical treatment of all existing Riemann solvers for compressible fluid dynamics and their use in the upwind method of Godunov and its high-order extensions. Related upwind methods of the Flux Vector Splitting type are also included, as are modern centred TVD methods. Methodologies for solving realistic problems in one, two and three space dimensions for both Cartesian and non-Cartesian geometries are presented in detail. Additional information is provided on further developments of the techniques and possible applications to practical problems in a variety of disciplines. A list of over 400 relevant references is given. The book is most useful for post-graduate students in Applied Mathematics, Engineering, Physics, Computing and other scientific disciplines such as Meteorology, Oceanography, Hydraulics and Chemistry, for example. It can be used as a means for self-study by academics and computational practioners in indusstry and research laboratories or as a teaching aid for postgraduate and final-year undergraduate courses on numerical methods etc. High resolution upwind and centered 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. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. For this third edition, the book was thoroughly revised. It contains substantial more and new material both in its fundamental as well as in its applied part