三阶HWCNS的构造及其在高超声速流动中的应用

Development of 3rd-order HWCNS and its application in hypersonic flow

对网格质量要求高、计算稳定性差和计算效率低是制约高阶精度格式应用于高超声速复杂流动模拟的重要因素。针对这些问题,发展了三阶精度的混合节点半节点加权紧致非线性格式（HWCNS3）,改进其光滑测试因子和非线性权得到了HWCNS3-OP,并给出了它们的频谱特性。利用Lax和Osher-Shu算例测试了格式对间断和高频波的捕捉能力;通过钝锥和航天飞机的高超声速绕流算例,考察了HWCNS3-OP在真实流动模拟中热流和气动力的预测精度及其计算效率。研究结果表明：HWCNS3-OP具有较高的分辨率和良好的间断捕捉能力,高频波捕捉能力相对HWCNS3提高了约3倍,相对守恒律的单调迎风中心格式（MUSCL）提高了约4倍;HWCNS3-OP计算稳定性较好,计算效率相对五阶HWCNS提高了2~3倍,HWCNS3-OP是一种较适合高超声速复杂流动模拟的高阶精度格式。

With very high requirements on computation grids, poor stability property and low computational efficiency, the application of high-order schemes to hypersonic flow simulations is greatly constrained. Focusing on these problems, a 3rd- order hybrid cell-node and cell-center weighted compact nonlinear schemes（HWONS3） is developed. Some improvements are made on the calculation of smoothness indicators and nonlinear weights, resulting in a new scheme named HWCNS3-OP. Spectral properties of different schemes are compared. Discontinuity capturing ability and high frequency waves＇ capturing ability are evaluated using Lax and Osher-Shu cases. After that HWCNS3-OP is applied to blunt cone and shuttle hypersonic flow simulations to study the prediction accuracy of heat flux and aerodynamic forces in relative practical cases. In these cases, the stability and efficiency property of HWCNS3-OP are investigated in priority. The results indicate that HWCNS3-OP has high resolution and good discontinuity capturing ability, the ability of simulating high frequency waves is improved by 3 times compared with HWCNS3 and by 4 times compared with monotonic upstream-centered scheme for conservation laws （MUSCL）, HWCNS3-OP is more stable, and that HWCNS3-OP＇s computational efficiency is improved by 2-3 times compared with HWCNS of 5th-order. HWCNS3-OP is a high-order scheme suitable for hypersonic flow simulations with complex grids.