边界层 $\alpha$-模型的微分代数框架
A Differential Algebraic Framework for Boundary Layer $α$-Models
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中文总结 AI 辅助
本文提出微分代数框架，通过区分Helmholtz算子作用，避免边界层解有限时间无限速度悖论，并得到近壁Taylor展开系数。
中文摘要 AI 辅助
通过解决描述Prandtl和Leray-$\alpha$边界层的饱和幺半群之间差异的问题，并在代数上区分Helmholtz算子的作用，我们可以证明，当矢量场的修改在由微分滤波器确定的最小尺度处停止时，构造在有限时间内达到无限速度的解的悖论得以避免。此外，该框架使我们能够获得已应用Helmholtz算子的边界层近壁处Taylor展开的系数。
英文摘要
By addressing the problem of describing the differences between the saturation monoids of the Prandtl and Leray-$α$ boundary layers, and algebraically distinguishing the action of the Helmholtz operator, we can show that, when the modification of the vector field is halted at a minimum scale determined by the differential filter, the paradox of constructing a solution that reaches infinite velocity in a finite time is avoided. Furthermore, it allows us to obtain the coefficients of the Taylor expansion near the wall for boundary layers where the Helmholtz operator has been applied.
发表机构
- Universidad Iberoamericana Ciudad de México（墨西哥城伊比利亚美洲大学）
机构由 AI 辅助整理，请以论文原文为准。
