Numerical Approximation of Hyperbolic Systems of Conservation Laws

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 publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

Revised version which completes the first 1996 publication Presents the state of the art concerning finite volume methods More examples and details added An expanding field Excellent up-to-date review of the current research trends in this area Rigorous theoretical framework for the numerical approximation of nonlinear hyperbolic systems of conservation laws by finite volume methods with emphasis on fluid models in the context of compressible flows

Inhalt
Nonlinear hyperbolic systems in one space dimension.- Gas dynamics and reacting flows.- Finite volume schemes for one-dimensional systems.- The case of multidimensional systems.- An introduction to boundary conditions.- Source terms.