Improved WENO Schemes for One-Dimensional Detonation Simulations

Based on three improved weighted essentially non-oscillatory (WENO) schemes, with WENO-Z scheme as the reference and using the different approach of nonlinear weight from the classical WENO scheme, the one-dimensional detonation systems under stable, slightly unstable and highly unstable cases were simulated; unlike the classical WENO scheme, these improved schemes overcame the problem of accuracy loss at critical points. The numerical results show that for the detonation systems in these three cases, the WENO-Z scheme, which is based on Lagrange polynomial reconstruct, is computationally stable and has the similar simulation results with the WENO-Z scheme, and is suitable for the simulation of detonation wave. For the stable and slightly unstable detonation systems, both the WENO-NS scheme and the WENO-P scheme have small oscillations, but they are computationally stable. However, for the highly unstable case, the WENO-NS scheme is computationally unstable, while its improved form, WENO-P scheme, is computationally stable.