Hybrid Fourier-Continuation method and WENO-Z finite difference scheme for multi-dimensional detonation structure simulations
Hybrid Fourier-Continuation method and WENO-Z finite difference scheme for multi-dimensional detonation structure simulations
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DOI：
10.4310/pamq.2018.v14.n1.a2
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发表时间：
2018
影响因子：
0.7
通讯作者：
Peng Li;Zhen Gao;W. Don
中科院分区：
文献类型：
--
作者：
Peng Li;Zhen Gao;W. Don
在（Li等人，J. Sci. Comput. 2015年，64：670-695），将傅里叶延拓（FC）方法与改进的五阶特征加权本质无振荡（WENO-Z）差分格式相结合，发展了求解双曲型守恒律方程组的一种混合FC-WENO-Z格式（Hybrid）。Hybrid格式用于保持WENO-Z格式以基本上无振荡的方式捕获显示高梯度和不连续性的解决方案部分，而光滑部分由线性的、基本上无耗散和无色散的FC方法高度分辨。利用Harten提出的高阶多分辨算法来度量解的光滑性。本文首次将Hybrid格式应用于包含不连续和复杂光滑结构的多维爆轰波结构的长时间数值模拟。实验中很好地捕捉到了爆轰波阵面后的精细尺度结构和半反应区峰值压力的准稳态胞格结构。一个经典的二维稳定爆轰波算例表明，与纯WENO-Z格式相比，Hybrid格式在计算爆轰波精细结构时具有更高的分辨率和更少的计算时间。文中还举例说明了初始条件和边界条件对爆轰波结构形成和演化的影响。最后，通过三维爆轰波数值模拟中的同相矩形、异相矩形和同相对角元胞结构，验证了Hybrid格式捕捉爆轰波阵面内在演化的能力，并与文献中已发表的结果进行了比较。
In (Li et al. J. Sci. Comput. 2015, 64: 670–695), a Hybrid FC-WENO-Z scheme (Hybrid) conjugating the FourierContinuation (FC) method with the improved fifth order characteristic-wise weighted essentially non-oscillatory (WENO-Z) finite difference scheme for solving the system of hyperbolic conservation laws was developed. The Hybrid scheme is used to keep the solutions parts displaying high gradients and discontinuities always captured by the WENO-Z scheme in an essentially non-oscillatory manner while the smooth parts are highly resolved by a linear, essentially non-dissipative and non-dispersive FC method. A high order multi-resolution algorithm by Harten is used for measuring the smoothness of the solutions. In this study, the Hybrid scheme is employed in the long time simulations of multi-dimensional detonation structures which contain both discontinuous and complex smooth structures for the first time. The fine scale structures behind the detonation front and the quasi-steady state cellular structures of the peak pressure in the half reaction zone are well captured. A classical stable two-dimensional detonation waves shows that an improved resolution of the more fine scale structures of detonation waves as computed by the Hybrid scheme with less CPU times when compares with the pure WENO-Z scheme. The influence of initial and boundary conditions on the formation and evolution of the detonation structures are also illustrated with examples. Finally, the in-phase rectangular, out-of-phase rectangular and in-phase diagonal cellular structures in the three-dimensional detonation simulations are shown to demonstrate the ability of the Hybrid scheme in capturing the intrinsic evolution of the detonation fronts, which are in good agreement with the published results in the literature.