The multiderivative combined dissipative compact scheme (MDCS) is extended to implement applications on complex curvilinear meshes. According to our previous evaluation on the scheme, a fifth-order MDCS, which has coexistent superior resolution power and relatively high efficiency, is chosen to present the performance of the MDCS. The capability of the fifth-order MDCS is evaluated by increasingly complex meshes in three typical tests: acoustic scattering from two cylinders, flow over a rod-airfoil configuration and flow over a landing gear model. On the curvilinear meshes, high resolution power possessed by the representative fifth-order MDCS is demonstrated for resolving acoustic wave. Moreover, the MDCS presents promising capability in simulating multiple scales in turbulent flow.