A general form of the dispersion-controlled dissipative (DCD) scheme is proposed.An unstructured DCD is constructed and its reliability is demonstrated with numerical simulations.Comparisons of the unstructured results with the second order structured results reveal that the previous resolution is well retained.In order to simulate detonation problems,unstructured DCD is combined with detailed chemical reaction kinetics.The algorithm is used to simulate detonation propagating along a straight duct with or without a wedge.Comparison of the numerical simulations and experiments shows that the algorithm works well in capturing detonation waves.Neither numerical oscillation nor artificial viscosity occurs in practical calculations.