Numerical Schemes for Conservation Laws (Wiley Series in Photoscience and Photoengineering) - Hardcover

Kröner, Dietmar

Hardcover

ISBN 10: 0471967939 ISBN 13: 9780471967934

Publisher: Wiley, 1997

Synopsis

This book systematically studies upwind methods for initial value problems for scalar conservation laws in one- and multidimensions. The mathematical theory of convergence theory and of a priori error estimates is presented in detail for structure (finite difference methods) as well as for unstructured grids (finite volume methods). Higher order schemes are also included. In the second part of the book the algorithms for scalar equations are generalized into systems of conversation laws in one- and multidimensions. The most powerful schemes for the discretization of systems are described and numerical examples are presented. In particular, local grid refinement has been taken into account. The initial boundary value problem is also considered for linear systems and nonlinear scalar conservation laws.

About this title

About the Author

Dietmar Kröner is the author of Numerical Schemes for Conservation Laws, published by Wiley.

From the Back Cover

Wiley-Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher Numerical Schemes for Conservation Laws Dietmar Kröner Albert-Ludwigs-Universität, Freiburg, Germany Many problems of fluid mechanics, in particular in gas-dynamics, have led to the study of non-linear hyperbolic conservation laws. Since the solutions of conservation laws may be discontinuous, even for smooth data, special stabilization techniques such as upwinding are necessary. This book systematically studies upwind methods for initial value problems for scalar conservation laws in one-and multidimensions. The mathematical theory of convergence theory and of a priori error estimates is presented in detail for structured grids (finite difference methods) as well as for unstructured grids (finite volume methods). Higher order schemes are also included. In the second part of the book the algorithms for scalar equations are generalized into systems of conservation laws in one- and multidimensions. The most powerful schemes for the discretization of systems are described and numerical examples are presented. In particular, local grid refinement has been taken into account. The initial boundary value problem is also considered for linear systems and nonlinear scalar conservation laws. Since nearly all mathematical details are developed and described in this book, it can be used as an introduction to the theory of upwind methods for conservation laws. Wiley Teubner

From the Inside Flap

Wiley-Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher Numerical Schemes for Conservation Laws Dietmar Kröner Albert-Ludwigs-Universität, Freiburg, Germany Many problems of fluid mechanics, in particular in gas-dynamics, have led to the study of non-linear hyperbolic conservation laws. Since the solutions of conservation laws may be discontinuous, even for smooth data, special stabilization techniques such as upwinding are necessary. This book systematically studies upwind methods for initial value problems for scalar conservation laws in one-and multidimensions. The mathematical theory of convergence theory and of a priori error estimates is presented in detail for structured grids (finite difference methods) as well as for unstructured grids (finite volume methods). Higher order schemes are also included. In the second part of the book the algorithms for scalar equations are generalized into systems of conservation laws in one- and multidimensions. The most powerful schemes for the discretization of systems are described and numerical examples are presented. In particular, local grid refinement has been taken into account. The initial boundary value problem is also considered for linear systems and nonlinear scalar conservation laws. Since nearly all mathematical details are developed and described in this book, it can be used as an introduction to the theory of upwind methods for conservation laws. Wiley Teubner

Edition details

• Publisher: Wiley
• Publication date: 1997
• Language: English
• ISBN 10: 0471967939
• ISBN 13: 9780471967934
• Binding: Hardcover
• Edition number: 1
• Number of pages: 520