Numerical Methods for One-Dimensional Hyperbolic Conservation Laws

摘要

The paper contains a survey of some important numerical methods for one-dimensional hyperbolic conservation laws. Weak solutions of hyperbolic conservation laws are introduced and the concept of entropy stability is discussed. Furthermore, the Riemann problem for hyperbolic conservation laws is solved. An introduction to numerical methods is given for which important concepts such as e.g. conservativity, stability and consistency are introduced. Godunov-type methods are elaborated for general systems of hyperbolic conservation laws. Finally, flux limiter methods are developed for the scalar non-linear conservation law.