Mathematical and Computational Methods for Compressible Flow(Numerical Mathematics and Scientific Computation) H 552 p. 03
Feistauer, Miloslav, Felcman, Jiri, Straskraba, Ivan 著
内容
目次
FUNDAMENTAL CONCEPTS AND EQUATIONS; 1.1 Some mathematical concepts andnotation; 1.2 Governing equations and relations of gas dynamics; 1.3 Someadvanced mathematical concepts and results; 1.4 Survey of concepts andresults from functional analysis; BASIC FACTS FROM THE THEORY OF THE EULERAND NAVIER-STOKES EQUATIONS; 2.1 Hyperbolic systems and the Euler equations;2.2 Existence of smooth solutions; 2.3 Weak solutions; 2.4 NonstationaryNavier-Stokes equations of compressible flow; 2.5 Existence results forstationary compressible Navier-Stokes equations; FINITE DIFFERENCE AND FINITEVOLUME METHODS FOR NON-LINEAR HYPERBOLIC SYSTEMS AND THE EULER EQUATIONS; 3.1Further properties of the Euler equations; 3.2 Numerical methods forhyperbolic systems with one space variable; 3.3 The finite volume method forthe multidimensional Euler equations; 3.4 Osher-Solomon scheme; 3.5 Higherorder finite volume schemes; 3.6 Adaptive methods; 3.7 Examples of finitevolume simulations; FINITE ELEMENT SOLUTION OF COMPRESSIBLE FLOW; 4.1 Finiteelement method - elementary treatment; 4.2 Finite element solution of viscousbarotropic flow; 4.3 Finite element solution of a heat conductive gas flow;4.4 Combined finite volume - finite element method for viscous compressibleflow; 4.5 Theory of the combined FV-FE method; 4.6 Discontinuous Galerkinfinite element method
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