A method for identifying a shock wave includes creating a grid comprising cells; sorting the cells based on their pressure gradients; and sorting the cells based on a negative dot product of their pressure gradients and their velocity vectors divided by the velocity of sound. The number of cells that are refined may be reduced by sorting the cells based on their distances from a shock wave center, and/or sorting the cells based on their mass fractions of a species. A buffer zone of refined cells may be created in front of the shock wave.