Numerical Methods for Conservation LawsBirkhäuser, 11 нояб. 2013 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. vVithout 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. |
Результаты поиска по книге
Результаты 1 – 5 из 50
Стр.
... . . . . . . . . 34 3.8 Entropy conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.8.1 Entropy functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4 Some Scalar Examples 41 4.1 Traffic flow ...
... . . . . . . . . 34 3.8 Entropy conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.8.1 Entropy functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4 Some Scalar Examples 41 4.1 Traffic flow ...
Стр.
... Solution of the Riemann problem ... entropy condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 ... solution of the Riemann problem . . . . . . . . . . . . . . . . . . . 86 8.4 Shock collisions ...
... Solution of the Riemann problem ... entropy condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 ... solution of the Riemann problem . . . . . . . . . . . . . . . . . . . 86 8.4 Shock collisions ...
Стр.
... Solutions 11.1 Modified equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 First order methods and diffusion ... entropy condition 13 Godunov's Method 13.1 The Courant-Isaacson-Rees method ...
... Solutions 11.1 Modified equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 First order methods and diffusion ... entropy condition 13 Godunov's Method 13.1 The Courant-Isaacson-Rees method ...
Стр. 9
... solution. For gas dynamics we can appeal to the second law of thermodynamics, which states that entropy is nondecreasing. In particular, as molecules of a gas pass through a shock their entropy should increase. It turns out that this ...
... solution. For gas dynamics we can appeal to the second law of thermodynamics, which states that entropy is nondecreasing. In particular, as molecules of a gas pass through a shock their entropy should increase. It turns out that this ...
Стр. 11
... solution even when discontinuities are present elsewhere. • Sharp resolution of discontinuities without excessive ... entropy condition, allowing us to conclude that the approximations in fact converge to the physically correct weak solution ...
... solution even when discontinuities are present elsewhere. • Sharp resolution of discontinuities without excessive ... entropy condition, allowing us to conclude that the approximations in fact converge to the physically correct weak solution ...
Содержание
1 | |
2 | |
14 | |
Some Scalar Examples | 41 |
Some Nonlinear Systems | 51 |
Linear Hyperbolic Systems | 58 |
Shocks and the Hugoniot Locus | 70 |
Rarefaction Waves and Integral Curves | 81 |
Computing Discontinuous Solutions | 114 |
Conservative Methods for Nonlinear Problems | 122 |
Godunovs Method | 136 |
Approximate Riemann Solvers | 146 |
Nonlinear Stability | 158 |
High Resolution Methods | 173 |
Semidiscrete Methods | 193 |
Multidimensional Problems | 200 |
The Riemann problem for the Euler equations | 89 |
Numerical Methods for Linear Equations | 97 |
Bibliography | 208 |
Другие издания - Просмотреть все
Часто встречающиеся слова и выражения
2-shock advection equation Buckley-Leverett equation Burgers cell average Chapter characteristic field characteristics compute conservation law consider contact discontinuity convergence convex define density derive differential equation discontinuous solutions discrete eigenvalues eigenvector entropy condition entropy solution entropy-satisfying Euler equations exact solution example EXERCISE flow flux function gas dynamics genuinely nonlinear gives Godunov's method grid Hugoniot locus initial data integral curve integral form isothermal equations jump Lax-Wendroff Lax-Wendroff method linear advection equation linear system matrix nonlinear systems Note numerical methods obtain particle paths phase plane piecewise constant pmax rarefaction wave requires Riemann problem scalar scalar conservation law scalar equations second order accurate shallow water equations shock speed shock wave shown in Figure smooth solutions ſº solution u(r,t space dimensions system of conservation system of equations term theorem total variation TV(U upwind method vanishing viscosity solution variables vector velocity viscosity solution weak solution