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.
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.
During the last decade enormous progress has been achieved in the field of computational fluid dynamics. This became possible by the development of robust and high-order accurate numerical algorithms...
Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite...
This book presents a new finite-difference scheme for hyperbolic conservation laws based on random choice. The authors show that this scheme outperforms conventional schemes in terms of accuracy and...
This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous...
The importance of hyperbolic conservation laws for scientific and industrial applications has led to a growing amount of research activity in this field. A variety of physical phenomena in fluid...
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