层流边界层中对流扰动的稳定高效单向建模：OWNS求和法
Stable and Efficient One-Way Modelling of Convective Disturbances in Laminar Boundary Layers: OWNS-Summation
浏览论文内容
中文总结 AI 辅助
本研究针对现有单向纳维-斯托克斯方法OWNS-R的误差放大与不稳定性问题，提出OWNS-S求和法，通过加性部分分式和避免乘法误差，可并行计算，在多类边界层上验证了其稳定性与精度。
中文摘要 AI 辅助
单向空间推进方法利用谱投影算子的有理近似，将上游与下游传播的扰动分离开来。在现有的单向纳维-斯托克斯（OWNS）公式中，递归变体OWNS-R最为经济，它将近似值计算为N个预解因子的乘积。该乘积会以乘法方式放大舍入误差，从而对近似阶数施加一个依赖于流动的上限，且该上限无法预先得知。我们将同一近似值重新表述为加性部分分式和（OWNS-Summation，OWNS-S）。在精确算术下，当提供相同的权重和极点时，递归计算与求和计算是等价的；但在浮点算术下，二者并不等价。N个预解算子求解中的每一个都作用于相同的输入状态，并对加权和做出独立贡献，从而避免了乘法误差放大。因此，近似阶数N成为纯粹的收敛参数，且各求解可并行运行。使用与OWNS-R相同的辅助极点，OWNS-S在所有测试构型中均保持精度，表明是递归计算而非极点是不稳定性的主要来源。我们还引入了配对贪心参数选择程序，其候选值取自上游和下游谱区域的解析估计，避免了空间推进过程中的特征值分解。OWNS-S在不可压缩、高超声速及跨声速边界层上得到验证。在跨声速情形中，扰动谱在推进过程中从亚声速拓扑重组为超声速拓扑，单向计算以抛物化稳定性方程无法达到的流向分辨率连续通过该转变。
英文摘要
One-way spatial marching methods separate upstream- from downstream-propagating disturbances using a rational approximation of a spectral projector. Among existing one-way Navier--Stokes (OWNS) formulations, the recursive variant, OWNS-R, is the most economical, evaluating the approximation as a product of $N$ resolvent factors. This product amplifies rounding errors multiplicatively, imposing a flow-dependent upper limit on the approximation order that cannot be known in advance. We reformulate the same approximation as an additive partial-fraction sum (OWNS-Summation, OWNS-S). In exact arithmetic, the recursive and summation evaluations are equivalent when supplied with identical weights and poles; in floating-point arithmetic, they are not. Each of the $N$ resolvent solves acts on the same input state and contributes independently to a weighted sum, preventing multiplicative error amplification. The approximation order $N$ therefore becomes a pure convergence parameter, and the solves can run in parallel. Using the same auxiliary poles as OWNS-R, OWNS-S remains accurate in every configuration tested, showing that the recursive evaluation, rather than the poles, is the dominant source of instability. A paired greedy parameter-selection procedure is also introduced, with candidates drawn from analytic estimates of the upstream and downstream spectral regions, avoiding eigen-decomposition during the numerical march. OWNS-S is validated on incompressible, hypersonic and transonic boundary layers. In the transonic case, the disturbance spectrum reorganises from a subsonic to a supersonic topology during the march. The one-way computation proceeds continuously through this transition at a streamwise resolution unattainable by the parabolised stability equations.
