Long time simulations are needed in the numerical study of the Zeldovich-Neumann-Döring model, in which the quality resolving the dynamics of the detonation front is crucial. The numerical error introduced from the inappropriate outflow boundary condition and the mesh resolution are two main factors qualitatively affecting the dynamics of the detonation front. In this paper we improve the numerical framework in [15] by introducing the Strang splitting method and a new h-adaptive method with a feature based a posteriori error estimator. Then a cheap numerical approach is proposed to sharply estimate a time period, in which the unphysical influence on the detonation front can be avoided effectively. The sufficiently dense mesh resolution can be guaranteed around the detonation front and in the reaction zone by the proposed h-adaptive method. The numerical results show that the proposed method is sufficiently robust even for long time calculations, and the quality dynamics of the detonation can be obtained by the proposed numerical approach.