Numerical Methods for Conservation LawsSpringer Science & Business Media, 13 февр. 1992 г. - Всего страниц: 214 These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy. |
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... methods • 11 Computing Discontinuous Solutions 11.1 Modified equations 11.1.1 First order methods and diffusion . 11.1.2 Second order methods and dispersion 11.2 Accuracy . 12 Conservative Methods for Nonlinear Problems 12.1 Conservative ...
... methods • 11 Computing Discontinuous Solutions 11.1 Modified equations 11.1.1 First order methods and diffusion . 11.1.2 Second order methods and dispersion 11.2 Accuracy . 12 Conservative Methods for Nonlinear Problems 12.1 Conservative ...
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V | 8 |
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XLI | 65 |
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C | 181 |
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Часто встречающиеся слова и выражения
1-shock advection equation approximate Riemann solution Buckley-Leverett equation Burgers cell average characteristic field characteristics coefficient compute conservation laws contact discontinuity convergence convex define density derive differential equations discrete eigenvalues eigenvector entropy condition Euler equations exact solution example finite difference fluid flux function gas dynamics gives Godunov's method grid Hugoniot locus hyperbolic initial data integral curve integral form ISBN jump Lax-Wendroff Lax-Wendroff method linear advection equation linear system Lipschitz continuous matrix modified equation nonlinear problems Note numerical methods numerical solution obtain piecewise constant piecewise linear Pmax propagating rarefaction wave Riemann problem satisfied scalar scalar conservation law second order accurate shallow water equations smooth solutions solution u(x solving system of equations systems of conservation t₁ theorem tn+1 total variation total variation diminishing truncation error TV(U u₁ Uj+1 Un+1 uo(x upwind method vanishing viscosity vector velocity viscosity solution weak solution
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