一种求解激波问题的中心差分-WENO混合方法研究

发布时间：2019-06-18 23:12

【摘要】：为提高求解包含激波问题的计算精度和效率,发展了一种低耗散、高效率的中心差分-WENO(Weighted Essentially Non-Oscillatory)混合格式,Navier-Stokes方程的无黏项在光滑流场区域采用六阶中心差分格式离散,而间断附近采用五阶WENO格式求解;基于密度设计了一种新型格式开关实现两种格式在光滑区域和间断之间自动切换,确保数值解在间断附近基本无振荡。针对一维激波熵波作用问题验证了混合格式的低耗散特性;对二维Riemann问题的研究表明发展的基于密度的格式开关更为合理,混合格式的计算效率较WENO格式明显提高;将其应用到激波诱导燃烧问题中,混合格式能很好地捕捉定常流场中激波和化学反应锋面的位置以及非定常流场的振荡频率。
[Abstract]:In order to improve the accuracy and efficiency of solving the problem including shock wave, a low dissipation and high efficiency central difference-WENO (Weighted Essentially Non-Oscillatory hybrid scheme is developed. The unviscous term of Navier-Stokes equation is discretized by the sixth-order central difference scheme in the smooth flow field region, while the fifth-order WENO scheme is used to solve the problem near the break. Based on the density, a new format switch is designed to realize the automatic switching between the two schemes in the smooth region and the discontinuity, so as to ensure that the numerical solution has no oscillations near the discontinuity. The low dissipation characteristics of the mixed scheme are verified for the one-dimensional shock entropy wave problem. The study of the two-dimensional Riemann problem shows that the developed density-based format switch is more reasonable, and the computational efficiency of the mixed scheme is obviously higher than that of the WENO scheme. When applied to the shock wave-induced combustion problem, the hybrid scheme can well capture the position of shock wave and chemical reaction front in the steady flow field and the oscillatory frequency of the unsteady flow field.
【作者单位】：国防科学技术大学高超声速冲压发动机技术重点实验室;
【基金】：国家自然科学基金(50906098)
【分类号】：O241.8;O354.5

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