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Numerical Schemes for Conservation Laws

By Dietmar Kröner

Product Image: Numerical Schemes for Conservation Laws

Numerical Schemes for Conservation Laws

By Dietmar Kröner

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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
Product details
Edition:
1
Number of Pages:
520
Release Date:
1997-01-15
Publication Date:
1997-03-06
Publisher:
Wiley
Languages:
Original: English
ISBN10:
0471967939
ISBN13:
9780471967934
GPSR Manufacturer Reference:
[email protected]
Weight:
1069 g
Height:
175 cm
Width:
250 cm
Thickness:
32 cm
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