The numerical simulations of one- and two-dimensional inviscid detonations for a stoichiometric ethylene/oxygen gas mixture are performed using the reduced chemical reaction model. VW model 1 and VW model 2 are accurate predictions for the ignition delay time compared with the UC San Diego model. Therefore, VW model 2 with 21 species is selected to simulate the ethylene-fueled detonation. The grid resolution study was validated, and it was found that the Zel'dovich-von Neumann-Doering (ZND) structure of the ethylene detonations contains H2O2 in a very short region. Comparing the species mole fraction profiles of one-dimensional analyses with those of the ZND structure, at least more than 10 points in the Delta H2O2 are required to estimate the chemical process accurately. This means that the grid width of three microns is suitable to simulate the detonations under the initial pressure of 0.01 MPa. The grid resolution of two-dimensional detonation simulations affects the detonation cell size as well as hydrogen-fueled detonations. In the case of a channel width d = 1 mm, the single-head detonations are adequately resolved for Delta = 3 mu m. However, the detonation cell width becomes irregular for d = 2 mm and Delta = 3 mu m.