An h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method with a
positivity-preserving technique to simulate classical two-dimensional detonation waves
is developed. The KXRCF troubled-cell indicator is used to detect the troubled cells with
possible discontinuities or high gradients. At each time-level, an adaptive mesh is generated by refining troubled cells and coarsening others. In order to avoid the situations
where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, a recursive multi-level mesh refinement technique is designed.
The numerical results show that for smooth solutions, this h-adaptive method does not
degrade the optimal convergence order of the nonadaptive method and outperforms it
in terms of computational storage for shocked flows.