The resulting structure generated by the interaction between the leading oblique detonation wave stabilized by a ramp and the expansion fan generated by a sudden deflection of the wedge surface is studied numerically. Simulations are carried out using a computer code that solves balance equations using an upwind cell-centred finite volume method on unstructured triangular meshes. The presence of shock waves and detonation waves on the flowfield requires the use of adaptive mesh techniques. The present work uses refinement and coarsening processes of the computational mesh. The former process improves the resolution in regions where the gradients of flowfield properties are high, while the latter one coarses the mesh in regions where the solution varies smoothly. It is demonstrated that the coarsening process that was implemented in this work leads to a reduction of computational time. In order to obtain parameters that lead to Chapman-Jouguet detonations as the result of the interaction, a quasi-one dimensional analysis of the combustion process is presented in terms of shock and detonation wave polars and of the induction time of the chemical kinetic mechan ism. Computations show that a Chapman-Jouguet oblique detonation wave may be obtained for intermediate wedge angles within the range of stable detonations. For wedge angles near to the maximum angle that supports stable detonations, decoupling of the oblique detonation wave is obtained which eventually leads to the extinction of the combustion process.