Reynolds‐averaged Navier‐Stokes simulations based on second‐order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin‐friction drag and aerodynamic heating, as well as in simulations of complex flows such as large‐scale separation and transition. A remedy for this is the development of high‐order schemes, by which numerically induced dissipation and dispersion errors of low‐order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high‐resolution nonlinear shock‐capturing methods. A stencil‐selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third‐order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh‐Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.

中文翻译：

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可压缩流模拟的三阶紧致非线性方案

基于二阶数值方法的雷诺平均Navier-Stokes模拟已被商业代码广泛使用，并作为大多数工业应用的主要工具。但是，它们在皮肤摩擦阻力和空气动力加热的准确可靠预测以及复杂流动（例如大规模分离和过渡）的模拟中受到限制。对此的一种补救方法是开发高阶方案，通过该方案可以有效地减少低阶方案的数值引起的耗散和色散误差。加权紧凑型非线性方案（WCNS）是一类高分辨率的非线性震动捕获方法。在拟议的工作中引入了模板选择程序，目的是提高三阶WCNS的非线性权重。通过使用近似色散关系分析，证明了与使用两个典型非线性权重的WCNS相比，新方案具有更低的耗散和色散误差。新方案在数值测试中也实现了改进，例如双重马赫反射问题和瑞利泰勒不稳定性仿真，分别以强烈的冲击不连续性和丰富的小尺度为特征。因此，该新方案在涉及强不连续性和多尺度现象的流动问题的仿真中受到高度青睐。新方案在数值测试中也实现了改进，例如双重马赫反射问题和瑞利泰勒不稳定性仿真，分别以强烈的冲击不连续性和丰富的小尺度为特征。因此，该新方案在涉及强不连续性和多尺度现象的流动问题的仿真中受到高度青睐。新方案在数值测试中也实现了改进，例如双重马赫反射问题和瑞利泰勒不稳定性仿真，分别以强烈的冲击不连续性和丰富的小尺度为特征。因此，该新方案在涉及强不连续性和多尺度现象的流动问题的仿真中受到高度青睐。