A Shock-fitting Primer

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Opis: A Shock-fitting Primer - Manuel D. Salas

A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. The book begins by recounting the events that lead to our understanding of the theory of shock waves and the early developments related to their computation. After presenting the main shock-fitting ideas in the context of a simple scalar equation, the author applies Colombeau's theory of generalized functions to the Euler equations to demonstrate how the theory recovers well-known results and to provide an in-depth understanding of the nature of jump conditions. He then extends the shock-fitting concepts previously discussed to the one-dimensional and quasi-one-dimensional Euler equations as well as two-dimensional flows. The final chapter explores existing and future developments in shock-fitting methods within the framework of unstructured grid methods. Throughout the text, the techniques developed are illustrated with numerous examples of varying complexity. On the accompanying CD-ROM, MATLAB(R) codes serve as concrete examples of how to implement the ideas discussed in the book.Introduction Prelude The Curious Events Leading to the Theory of Shock Waves Early Attempts at Computing Flows with Shocks Shock-Fitting Principles The Inviscid Burgers' Equation The One-Saw-Tooth Problem Background Numerical Schemes Mappings, Conservation Form, and Transformation Matrices Boundary Shock-Fitting Gaussian Pulse Problem Boundary Shock-Fitting Revisited Floating Shock-Fitting Detection of Shock Formation Application of Colombeau's Generalized Functions to a Nonconservative System of Equations Fundamental Concepts and Equations Physical Problem Mathematical Formulation Explicit Form of the Equations of Motion Orthogonal Curvilinear Coordinates Differential Geometry of Singular Surfaces Finite Discontinuities Shock Wave Structure Euler Equations: One-Dimensional Problems Piston-Driven Flows Numerical Analysis of a Simple Wave Region Shock Wave Computation Quasi-One-Dimensional Flows Euler Equations: Two-Dimensional Problems The Blunt Body Problem External Conical Corners Supersonic Flow over Elliptical Wings Floating Shock-Fitting with Unstructured Grids Introduction Unstructured Grids: Preliminaries Unstructured Grid Solver Application to Euler Equations Floating Shock-Fitting Implementation Unstructured Grids Shock-Fitting Results References Appendix Index Problems appear at the end of each chapter.


Szczegóły: A Shock-fitting Primer - Manuel D. Salas

Tytuł: A Shock-fitting Primer
Autor: Manuel D. Salas
Producent: CRC Press Inc.
ISBN: 9781439807583
Rok produkcji: 2009
Ilość stron: 416
Oprawa: Twarda
Waga: 0.75 kg


Recenzje: A Shock-fitting Primer - Manuel D. Salas

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A Shock-fitting Primer

A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. The book begins by recounting the events that lead to our understanding of the theory of shock waves and the early developments related to their computation. After presenting the main shock-fitting ideas in the context of a simple scalar equation, the author applies Colombeau's theory of generalized functions to the Euler equations to demonstrate how the theory recovers well-known results and to provide an in-depth understanding of the nature of jump conditions. He then extends the shock-fitting concepts previously discussed to the one-dimensional and quasi-one-dimensional Euler equations as well as two-dimensional flows. The final chapter explores existing and future developments in shock-fitting methods within the framework of unstructured grid methods. Throughout the text, the techniques developed are illustrated with numerous examples of varying complexity. On the accompanying CD-ROM, MATLAB(R) codes serve as concrete examples of how to implement the ideas discussed in the book.Introduction Prelude The Curious Events Leading to the Theory of Shock Waves Early Attempts at Computing Flows with Shocks Shock-Fitting Principles The Inviscid Burgers' Equation The One-Saw-Tooth Problem Background Numerical Schemes Mappings, Conservation Form, and Transformation Matrices Boundary Shock-Fitting Gaussian Pulse Problem Boundary Shock-Fitting Revisited Floating Shock-Fitting Detection of Shock Formation Application of Colombeau's Generalized Functions to a Nonconservative System of Equations Fundamental Concepts and Equations Physical Problem Mathematical Formulation Explicit Form of the Equations of Motion Orthogonal Curvilinear Coordinates Differential Geometry of Singular Surfaces Finite Discontinuities Shock Wave Structure Euler Equations: One-Dimensional Problems Piston-Driven Flows Numerical Analysis of a Simple Wave Region Shock Wave Computation Quasi-One-Dimensional Flows Euler Equations: Two-Dimensional Problems The Blunt Body Problem External Conical Corners Supersonic Flow over Elliptical Wings Floating Shock-Fitting with Unstructured Grids Introduction Unstructured Grids: Preliminaries Unstructured Grid Solver Application to Euler Equations Floating Shock-Fitting Implementation Unstructured Grids Shock-Fitting Results References Appendix Index Problems appear at the end of each chapter.

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Cena 532,00 PLN
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