Giesekus 粘滑奇异性：对数构象表述中的渐近理论
Giesekus Stick-Slip Singularity: Asymptotic Theory in the Log-Conformation Formulation
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中文总结 AI 辅助
本文首次将对数构象表述用于Giesekus流体粘滑奇点的渐近分析，扩展了现有理论，获得了奇点附近一致有效的复合渐近解。
中文摘要 AI 辅助
本文对平面粘滑奇点附近的 Giesekus 流体的对数构象重构进行了分析研究。据我们所知，这是首次将对数构象表述用于其数值目的之外，我们在给定牛顿速度场的假设下，给出了与 Evans [JNNFM 222 (2015) 24-33] 在粘附、滑移和核心区域的渐近应力分析相匹配的结果。此外，对数重构使我们能够大幅扩展现有的渐近理论，例如，表明构象张量的行列式渐近恒定，并彻底表征了边界层与核心区域之间的过渡行为。结合这些结果，我们获得了对数构象方程的复合渐近解，该解在奇点的紧邻区域内一致有效。
英文摘要
In this paper, the log-conformation reformulation of a Giesekus fluid near a planar stick-slip singularity is investigated analytically. In what is, to our knowledge, the first use of the log-conformation formulation beyond its numerical purpose, we present results that match the asymptotic stress analysis of Evans [JNNFM 222 (2015) 24-33] for the stick, slip, and core regions under the assumption of a given Newtonian velocity field. Furthermore, the logarithmic reformulation allows us to extend the existing asymptotic theory substantially, showing, e.g., that the determinant of the conformation tensor is asymptotically constant, as well as thoroughly characterizing the transition behavior between the boundary layers and the core region. Combining these results, we obtain a composite asymptotic solution of the log-conformation equation that is valid uniformly throughout a close neighborhood of the singularity.
发表机构
- German Aerospace Center (DLR), Institute of Software Technology, Department of High-Performance Computing（德国航空航天中心（DLR）软件技术研究所高性能计算系）
机构由 AI 辅助整理，请以论文原文为准。
