$\delta-$Wave for 1-D and 2-D Hyperbolic Systems

Abstract

Here a new kind of nonlinear wave, which is called $\delta-$wave, is described by some high resolution difference solutions for Riemann problems of one-dimensional (1-D) and two-dimensional (2-D) nonlinear hyperbolic systems in conservation laws. Some phenomena are numerically shown for the solutions of Riemann problems for 2-D gas dynamics systems.