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守恒定律用的数值法PDF|Epub|txt|kindle电子书版本网盘下载
- （美）勒维克著 著
- 出版社： 世界图书北京出版公司
- ISBN：9787510027406
- 出版时间：2010
- 标注页数：214页
- 文件大小：39MB
- 文件页数：225页
- 主题词：双曲型方程－数值计算－英文
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图书目录
1 Introduction1
1.1 Conservation laws1
1.2 Applications2
1.3 Mathematical difficulties8
1.4 Numerical difficulties9
1.5 Some references12
2 The Derivation of Conservation Laws14
2.1 Integral and differential forms14
2.2 Scalar equations16
2.3 Diffusion17
3 Scalar Conservation Laws19
3.1 The linear advection equation19
3.1.1 Domain of dependence20
3.1.2 Nonsmooth data21
3.2 Burgers' equation23
3.3 Shock formation25
3.4 Weak solutions27
3.5 The Riemann Problem28
3.6 Shock speed31
3.7 Manipulating conservation laws34
3.8 Entropy conditions36
3.8.1 Entropy functions37
4 Some Scalar Examples41
4.1 Traffic flow41
4.1.1 Characteristics and "sound speed"44
4.2 Two phase flow48
5 Some Nonlinear Systems51
5.1 The Euler equations51
5.1.1 Ideal gas53
5.1.2 Entropy54
5.2 Isentropic flow55
5.3 Isothermal flow56
5.4 The shallow water equations56
6 Linear Hyperbolic Systems58
6.1 Characteristic variables58
6.2 Simple waves60
6.3 The wave equation60
6.4 Linearization of nonlinear systems61
6.4.1 Sound waves63
6.5 The Riemann Problem64
6.5.1 The phase plane67
7 Shocks and the Hugoniot Locus70
7.1 The Hugoniot locus70
7.2 Solution of the Riemann problem73
7.2.1 Riemann problems with no solution75
7.3 Genuine nonlinearity75
7.4 The Lax entropy condition76
7.5 Linear degeneracy78
7.6 The Riemann problem79
8 Rarefaction Waves and Integral Curves81
8.1 Integral curves81
8.2 Rarefaction waves82
8.3 General solution of the Riemann problem86
8.4 Shock collisions88
9 The Riemann problem for the Euler equations89
9.1 Contact discontinuities89
9.2 Solution to the Riemann problem91
Ⅱ Numerical Methods95
10 Numerical Methods for Linear Equations97
10.1 The global error and convergence102
10.2 Norms103
10.3 Local truncation error104
10.4 Stability106
10.5 The Lax Equivalence Theorem107
10.6 The CFL condition110
10.7 Upwind methods112
11 Computing Discontinuous Solutions114
11.1 Modified equations117
11.1.1 First order methods and diffusion118
11.1.2 Second order methods and dispersion119
11.2 Accuracy121
12 Conservative Methods for Nonlinear Problems122
12.1 Conservative methods124
12.2 Consistency126
12.3 Discrete conservation128
12.4 The Lax-Wendroff Theorem129
12.5 The entropy condition133
13 Godunov's Method136
13.1 The Courant-Isaacson-Rees method137
13.2 Godunov's method138
13.3 Linear systems140
13.4 The entropy condition142
13.5 Scalar conservation laws143
14 Approximate Riemann Solvers146
14.1 General theory147
14.1.1 The entropy condition148
14.1.2 Modified conservation laws149
14.2 Roe's approximate Riemann solver149
14.2.1 The numerical flux function for Roe's solver150
14.2.2 A sonic entropy fix151
14.2.3 The scalar case153
14.2.4 A Roe matrix for isothermal flow156
15 Nonlinear Stability158
15.1 Convergence notions158
15.2 Compactness159
15.3 Total variation stability162
15.4 Total variation diminishing methods165
15.5 Monotonicity preserving methods165
15.6 l1-contracting numerical methods166
15.7 Monotone methods169
16 High Resolution Methods173
16.1 Artificial Viscosity173
16.2 Flux-limiter methods176
16.2.1 Linear systems182
16.3 Slope-limiter methods183
16.3.1 Linear Systems187
16.3.2 Nonlinear scalar equations188
16.3.3 Nonlinear Systems191
17 Semi-discrete Methods193
17.1 Evolution equations for the cell averages193
17.2 Spatial accuracy195
17.3 Reconstruction by primitive functions196
17.4 ENO schemes198
18 Multidimensional Problems200
18.1 Semi-discrete methods201
18.2 Splitting methods202
18.3 TVD Methods206
18.4 Multidimensional approaches206
Bibliography208