Numerical Methods for Conservation Laws

Front Matter....Pages i-viii
Front Matter....Pages ix-ix
Introduction....Pages 1-13
The Derivation of Conservation Laws....Pages 14-18
Scalar Conservation Laws....Pages 19-40
Some Scalar Examples....Pages 41-50
Some Nonlinear Systems....Pages 51-57
Linear Hyperbolic Systems....Pages 58-69
Shocks and the Hugoniot Locus....Pages 70-80
Rarefaction Waves and Integral Curves....Pages 81-88
The Riemann problem for the Euler equations....Pages 89-93
Front Matter....Pages 95-95
Numerical Methods for Linear Equations....Pages 97-113
Computing Discontinuous Solutions....Pages 114-121
Conservative Methods for Nonlinear Problems....Pages 122-135
Godunov’s Method....Pages 136-145
Approximate Riemann Solvers....Pages 146-157
Nonlinear Stability....Pages 158-172
High Resolution Methods....Pages 173-192
Semi-discrete Methods....Pages 193-199
Multidimensional Problems....Pages 200-207
Back Matter....Pages 208-214