An adaptive grid method which redistributes grid points according to equidistribution principle was implemented to an in-house computational fluid dynamics code capable of simulating blast waves. The resultant code was first tested for a shock tube problem. It was observed that benefit of using adaptive grids becomes more evident when discontinuities in the flow are stronger. It was also observed that interpolation method used to move the flow variables to new grid locations directly affects the accuracy of the solution and interpolation methods which do not guarantee conservation of mass may yield highly inaccurate results. Blast wave simulations performed showed that the adaptive grid method used here improved predictions considerably without requiring a lot of extra CPU time.