In the numerical modeling of divergent detonation, the matched relationship between the viscosity and the mesh size was studied in terms of the Lee-Tarver′s reaction rate and JWL equation of state. The results indicate that the artificial viscosity is higher near the center and tends to be one dimensienal plane far from the center. Moreover,spherical divergent detonation of PBX-9404 explosive was simulated. And the results are in agreement with the characteristics of divergent detonation.