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摘要:
在计算流体力学（CFD）方法中，限制技术是影响计算精度和计算稳定性的重要因素，目前应用较广的经典二阶总变差衰减（TVD）限制器虽能较好地满足计算要求，但性能差异大且分辨率和耗散的性能间并未得到良好权衡。对一种新型的三阶TVD插值限制器（T-3限制器）进行了研究并将其与3种经典限制器进行对比。首先通过一维黎曼问题，得出T-3限制器兼顾较高间断分辨率和良好稳定性的特点；接着通过高超声速双锥绕流和X-33外形飞行器的数值实验，得到T-3限制器具有刻画复杂流动的能力以及较优的气动热计算性能。
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关键词:
- 限制器 /
- 计算流体力学 (CFD) /
- 激波 /
- 双锥绕流 /
- 气动热
Abstract:For numerical scheme in computational fluid dynamics (CFD), limiter technology is an important factor affecting computational accuracy and stability. Although the present classical second-order total variation diminishing (TVD) limiters with a wide application can well satisfy the computing requirements, its performance not only largely differs but also cannot be properly weighted between resolution and dissipation. Therefore, a new third-order TVD interpolation limiter (T-3 limiter) has been studied and compared with three classical limiters. First, through one-dimensional Riemann problem, it has been found that T-3 limiter is simultaneously characterized by both high intermittent resolution and excellent stability; then, by numerical simulation of hypersonic flow over a double-cone body and X-33 configuration, it has been found that T-3 limiter boasts the capability of portraying complex flow and good aerothermodynamic calculation performance.
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Key words:
- limiter /
- computational fluid dynamics (CFD) /
- shocks /
- double-cone disturbance flow /
- aerothermodynamic
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图 4 壁面压强沿母线分布曲线
Figure 4. Distribution curves of wall surface pressure along generating line
图 5 40°迎角下对称面等马赫线图和壁面压强云图
Figure 5. Mach contours in symmetry plane and wall surface pressure contours at α=40°
图 7 迎风区子午线热流分布与实验值的对比
Figure 7. Comparison between windward centerline heat flow distribution and experimental data
表 1 分离点、再附点、分离区长度的计算结果
Table 1. Calculated separation position, reattachment position and separation zone length
限制器 x/L 分离点 再附点 分离区长度 minmod 0.597 5 1.103 5 0.506 double minmod 0.565 8 1.164 1 0.598 superbee 0.505 0 1.151 1 0.646 T-3 0.449 1 1.095 0 0.646 
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表 2 壁面压强峰值计算结果
Table 2. Calculated results of wall surface pressure peak
限制器 峰值位置 (x/L) 位置误差/% 压强峰值 (p/p∞) 峰值误差/% 实验 1.424 5 104.698 minmod 1.358 5 4.633 0 94.307 9.925 double minmod 1.429 6 0.358 0 94.689 9.560 superbee 1.437 5 0.913 0 107.886 3.045 T-3 1.498 5 1.825 0 102.831 1.783
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