FEM software has been well-developed in shock wave simulation. As the software usually is huge and complicated, subdivision mesh needs lots of computation, and the precision is not assured, finite-difference methods are highly regarded. Difference schemes are related to the stability and precision. In this paper, a Lax-Friedrichs based difference method is presented. Different grids were discussed and the numerical results were compared with Henrych empirical formula. Furthermore, comparing the data from numerical simulation of TNT explosive and the data from DYNA software, we concluded finite-difference methods have advantage of FEM methods.