An implementation of Runge-Kutta Discontinuous Galerkin method was performed to simulate flows with strong discontinuities. The method was tested for a planar shock tube problem with extremely strong discontinuities, and numerical solutions were compared with predictions of a finite volume method and exact solutions. It was observed that when there are strong discontinuities in the flowfield, the limiter function adopted for solution clearly affects the overall quality of the predictions. An alternative limiting strategy, which uses combination of different limiters for different flow variables, was tested and great improvements in the solutions were observed. The method was also extended to moving adaptive grids by using Arbitrary Lagrangian-Eulerian formulation. Blast waves generated by an explosion were also simulated with and without including high temperature effects for surrounding air. Despite the high temperatures encountered, using calorically perfect gas assumption for air did not produce negative consequences.