Machine derived contents note: Fundamental concepts and equations -- 1.1. Some mathematical concepts and notation -- 1.2. Governing equations and relations of gas dynamics -- 1.3. Some advanced mathematical concepts and results -- 1.4. Survey of concepts and results from functional analysis -- Basic facts from the theory of the Euler and Navier-Stokes equations -- 2.1. Hyperbolic systems and the Euler equations -- 2.2. Existence of smooth solutions -- 2.3. Weak solutions -- 2.4. Nonstationary Navier-Stokes equations of compressible flow -- 2.5. Existence results for stationary compressible Navier-Stokes equations -- Finite difference and finite volume methods for non-linear hyperbolic systems and the Euler equations -- 3.1. Further properties of the Euler equations -- 3.2. Numerical methods for hyperbolic systems with one space variable -- 3.3. The finite volume method for the multidimensional Euler equations -- 3.4. Osher-Solomon scheme -- 3.5. Higher order finite volume schemes -- 3.6. Adaptive methods -- 3.7. Examples of finite volume simulations -- Finite element solution of compressible flow -- 4.1. Finite element method - elementary treatment -- 4.2. Finite element solution of viscous barotropic flow -- 4.3. Finite element solution of a heat conductive gas flow -- 4.4. Combined finite volume - finite element method for viscous compressible flow -- 4.5. Theory of the combined FV-FE method -- 4.6. Discontinuous Galerkin finite element method
Bibliography
Includes bibliographical references (pages 507-528) and index
