光滑型TENO非线性加权六阶低耗散WCNS-CU6-ST格式
收稿日期: 2024-04-24
修回日期: 2024-05-13
录用日期: 2024-07-09
网络出版日期: 2024-08-05
基金资助
国家自然科学基金(52376114);国家科技重大专项(2017-III-0005-0029)
Sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth TENO nonlinear weight
Received date: 2024-04-24
Revised date: 2024-05-13
Accepted date: 2024-07-09
Online published: 2024-08-05
Supported by
National Natural Science Foundation of China(52376114);National Science and Technology Major Project(2017-III-0005-0029)
空天飞行器的流动环境涉及激波与湍流等复杂流动现象，流场中激波间断与多尺度湍流结构共存使得高阶精度数值模拟面临巨大挑战。为了提升对复杂湍流流动问题模拟的精度，在加权紧致非线性格式（WCNS）框架下，发展了六阶中心/五阶迎风线性混合插值方法；同时考虑到高分辨率的激波捕捉特性，TENO格式中的尺度分离策略被用于发展非线性权函数，针对数值格式的数值收敛性，进一步发展了光滑型S-TENO非线性权函数。通过近似色散关系（ADR）、一维流动问题、三维槽道湍流和跨声速翼型自适应湍流模拟的算例测试，发现线性模板采用六阶中心/五阶迎风的混合插值方法，能够显著降低格式的数值耗散，从而改善槽道湍流的预测精度；同时光滑型S-TENO非线性权函数不仅保持了原TENO格式非线性权函数良好的色散耗散特性，并在跨声速翼型流动的激波/湍流边界层干扰模拟算例中，提升了数值收敛性，数值算例结果表明本文提出的基于光滑型S-TENO权函数的六阶低耗散WCNS-CU6-ST格式能够同时具备数值耗散低与收敛良好的数值特性，有助于进一步提升对激波/湍流等复杂流动问题模拟的准确性。
吴文昌 , 韩省思 , 闵耀兵 , 燕振国 , 马燕凯 . 光滑型TENO非线性加权六阶低耗散WCNS-CU6-ST格式[J]. 航空学报, 2024 , 45(S1) : 730598 -730598 . DOI: 10.7527/S1000-6893.2024.30598
The flow environment of spacecraft involves complex flow phenomena such as shock waves and turbulence. The coexistence of shock wave discontinuities and multiscale turbulent structures in the flow field poses significant challenges to high-order accurate numerical simulations. To effectively reduce numerical dissipation in turbulence simulations， a sixth-order central/fifth-order upwind linear hybrid interpolation was developed under the framework of Weighted Compact Nonlinear Scheme （WCNS）. Considering the high-resolution shock capturing characteristics， the scale separation strategy in the TENO scheme is used to develop nonlinear weight functions. For the numerical convergence of the numerical scheme， a smooth S-TENO nonlinear weight function is further developed. Through Approximate Dispersion Relations （ADR）， one-dimensional convection problems， and self-adaptive turbulence eddy simulation of three-dimensional channel， it was found that the linear stencil using a sixth-order central/fifth-order upwind linear hybrid interpolation stencil can significantly reduce the numerical dissipation of the scheme， thereby improving the prediction accuracy of channel flow and transonic flow past an airfoil. The proposed smooth S-TENO nonlinear weight not only maintains the good dispersion and dissipation properties of the original TENO nonlinear weight， but also significantly improves the numerical convergence in the cases of shock wave/turbulent boundary layer interaction when transonic flow past an airfoil， thus improving the accuracy of computational results. The numerical results indicate that the optimized sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth S-TENO weight can achieve both low numerical dissipation and good convergence， which is helpful to improve the accuracy of simulations in complex shock/turbulence problems.
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