适用于曲线网格上可压缩Navier-Stokes方程的、带隐式时间积分的高分辨率加权本质非振荡紧致最小二乘格式
High-Resolution Weighted Essentially Non-Oscillatory Compact Least-Squares Schemes with Implicit Time Integration for Compressible Navier-Stokes Equations on Curvilinear Grids
AI总结：
本文提出带隐式时间积分的高分辨率加权本质非振荡紧致最小二乘格式，用于曲线网格上可压缩Navier-Stokes方程，可高效捕获激波并在光滑区域保持高分辨率，性能优于传统格式。
AI中文摘要：
本文针对曲线网格上的可压缩Navier-Stokes方程，提出了一系列带隐式时间积分的高分辨率加权本质非振荡紧致最小二乘格式。与原始紧致最小二乘格式相比，该方法引入了两项主要改进：其一，它未在包含间断区域的整个计算域上施加精度约束，而是采用保精度加权策略仅沿光滑重构线构造重构矩阵，该处理有效抑制了原始紧致最小二乘格式中持续存在的高频振荡，并在间断附近产生更锐利的剖面；其二，该方法使用单一多项式集简化了激波捕获过程并提升了效率，而原始紧致最小二乘格式则需要同时使用无限制和受限多项式。结合谱优化，所提方法展现出比传统加权本质非振荡格式更优的谱特性。光滑性指标与罚矩阵通过高效迭代过程构造，仅需适度额外成本。无粘和粘性的一维、二维、三维流动的数值结果表明，所提方法具备稳健的激波捕获能力，同时在光滑区域及接触间断处保持高分辨率。
英文摘要：
This paper presents a family of high-resolution weighted essentially non-oscillatory compact least-squares schemes with implicit time integration for the compressible Navier-Stokes equations on curvilinear grids. Compared with the original compact least-squares schemes, the proposed method introduces two main improvements. First, instead of enforcing the accuracy constraints over the entire computational domain, including discontinuous regions, it constructs the reconstruction matrix only along smooth reconstruction lines using an accuracy-preserving weighting strategy. This treatment effectively suppresses the persistent high-frequency oscillations observed in the original compact least-squares schemes and yields sharper profiles near discontinuities. Second, the method simplifies the shock-capturing procedure and improves efficiency by using a single set of polynomials, whereas the original compact least-squares schemes require both unlimited and limited polynomials. Combined with spectral optimization, the proposed method exhibits more favorable spectral properties than conventional weighted essentially non-oscillatory schemes. The smoothness indicators and penalty matrices are constructed through an efficient iterative procedure with modest additional cost. Numerical results for inviscid and viscous one-, two-, and three-dimensional flows demonstrate that the proposed method provides robust shock-capturing capability while maintaining high resolution in smooth regions and across contact discontinuities.
