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This book details algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. Includes programming exercises.

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Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.

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Introduction.- Background.- Overview and Roadmap.- Fundamentals.- Model Equations.- Finite-Difference Methods.- The Semi-Discrete Approach.- Finite-Volume Methods.- Numerical Dissipation and Upwind Schemes.- Time-Marching Methods for ODEs.- Stability Analysis.- Governing Equations.- The Euler and Navier-Stokes Equations.- The Reynolds-Averaged Navier-Stokes Equations.- The Quasi-One-Dimensional Euler Equations and the Shock-Tube Problem.- Exercises An Implicit Finite-Difference Algorithm.- Introduction.- Generalized Curvilinear Coordinate Transformation.- Thin-Layer Approximation.- Spatial Differencing.- Implicit Time Marching and the Approximate Factorization Algorithm.- Boundary Conditions.- Three-Dimensional Algorithm.- One-Dimensional Examples.- Summary.- Appendix: Flux Jacobian Eigensystems in Two and Three Dimensions.- An Explicit Finite-Volume Algorithm with Multigrid.- Introduction.- Spatial Discretization: Cell-Centered Finite-Volume Method.- Iteration to Steady State.- One-Dimensional Examples.- Summary.- Exercises.- Introduction to High-Resolution Upwind Schemes.- Introduction.- Godunov´s Method.- Roe´s Approximate Riemann Solver.- Higher-Order Reconstruction.- Conservation Laws and Total Variation.- Monotone and Monotonicity-Preserving Schemes.- Total-Variation-Diminishing Conditions.- Total-Variation-Diminishing Schemes with Limiters.- One-Dimensional Examples.- Summary.- Exercises.- References.- Index.

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"The text is supplemented with illustrative exercises that serve to reinforce concepts and methods of treating such problems and to discuss some techniques related to the discretization of equations and treatment, and formulating and solving them. If the book was intended to be used as a text book, its objectives have been largely achieved ... . This is a book that can lend important help to those working in the subject." (Melio Sáenz, Research Gate, researchgate.net, June, 2016)

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