This aim of this study is to investigate the effect of grid resolution and higher-order accuracy schemes. The size of the reaction induction zone at the time of the local explosion affects the generation of transverse cells. When the reaction zone is large, transverse cells appear. As a result, for calculations in which the grid width is small or for a higher-order scheme, such as a weighted compact nonlinear scheme (WCNS), is used, the cell size increases; an irregular cellular structure is obtained, such as that observed in experiments; and unburned gas pockets and circulation structures caused by Kelvin-Helmholtz instability appear behind the detonation front. In terms of the computational cost, the computational time of 7th-orderWCNSis approximately three times that of the 2nd-order monotone upstream-centered schemes for conservation laws (MUSCL) scheme.