Grid resolution considerations for simulating non-ideal cellular detonations

3D high-fidelity simulations of non-ideal detonations in narrow channels are conducted in this study to assess the numerical resolution requirement for capturing both viscous and thermal wall losses. 3D simulations are complimented with auxiliary 2D simulations of the narrow dimension of the channel. A comprehensive convergence study, with grid resolutions ranging from 11 to 357 cells per ZND induction length was performed. A brief scale analysis was performed using Mirels’ boundary layer solution, which provides a framework for estimating the resolution requirements for a non-ideal detonation simulation. The impact of grid resolution and boundary condition was quantitatively assessed through measurement of the average detonation wave speed, analysis of average boundary layer profiles, and comparison of the effective local volumetric momentum and heat loss terms. By filtering Mirels’ solution, the loss terms from simulation were accurately recreated. This provides a mechanism to predict the error in detonation wave speed based on grid resolution. Using the filtered Mirels’ model, a simulation resolution criterion is proposed, requiring the grid resolution to be at least the momentum thickness evaluated at one induction length after the lead shock.