改进型WENO格式的一维爆轰波数值模拟

基于3种改进型加权本质无振荡（WENO）格式，以5阶的WENO-Z格式为参考，采用与经典WENO格式不同形式的非线性权重计算方法，对稳定、中度不稳定和高度不稳定状态下的1维爆轰波系统进行了数值模拟，克服了经典的WENO格式在计算临界点时精度降低的问题.数值实验表明，对于3种状态下的爆轰系统，基于Lagrange多项式重构的WENO-Zη格式计算稳定性好，模拟效果与WENO-Z格式较为一致，比较适合于爆轰波的数值模拟.对于稳定和中度不稳定的爆轰系统，WENO-NS格式和WENO-P格式在数值模拟中会出现小的数值振荡，但计算稳定；而对于高度不稳定爆轰系统，WENO-NS格式计算不稳定，其改进形式WENO-P格式计算稳定性较好. 

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.