Arbitrary-Order High Resolution Schemes for Model Hyperbolic Conservation Laws

摘要

The general theory and methodology of high resolution numerical schemes for onedimensional hyperbolic conservation laws are investigated. The universal formula from which two level explicit conservative arbitrary order numerical methods can be derived is developed. The issue of linear stability is considered. A new approach to linear stability analysis is presented. The generalized formulation for total variation diminishing methods with stable region of c between -1 and 1 is proposed. To demonstrate the theories, third order and fourth order total variation diminishing methods are generated. Computational results of these schemes show features of high resolution methods.