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航空航天工程系学术报告

题目：Two-scale Approach to Turbulence Closure for Wall-modelled LES—Some ‘Known Unknowns’ and/or ‘Unknown Knowns’?

报告人Prof. Li He(何力)

University of Oxford

主持人：黄迅 教授

时间：2025年12月19日（周五）上午10:30-11:30

地点：新奥工学大楼1F-1006会议室

报告人简介：

Professor He was trained as an aeronautical engineer (BSc 1982, MSc 1984 at BUAA, and Ph.D 1990 at Cambridge). He had worked in the three oldest universities in England (Cambridge,1990-1993, Durham 1993-2007 and Oxford 2008-2025), and recently retired from his chair as the Statutory Professor of Computational Aerothermal Engineering at Oxford. Having spent much of his career on applied research in novel methods development for practical applications, he has become increasingly interested in more fundamental aspects of methodologies and basic aerothermal physical understanding (rather than often ‘over-emphasized’ details & specifics!).

报告内容摘要：

For wall-bounded turbulent flow, a question of close relevance is: how should the inner near-wall region be dealt with computationally? A prevalent wisdom of the near-wall region being dominated by a self-sustained autonomous dynamic ‘universal’ behaviour, had served as a strong motivation for RANS based Wall-modelled LES (WMLES) with much coarser nearwall mesh. Similarly the nearwall region may be solved with LES without a RANS model at all. In this case the LES solution is subject to a specially developed/tuned (via AI/ML or other data-driven/empirical means) wall function. The latter is so called Wall Function conditioned LES (WFLES).

It has to be noted that the cost benefit of WMLES/WFLES by using a coarse mesh in the near wall region will inevitably be tied to its own price in under-resolution associated numerical errors. The very mesh-dependent nature of the errors means that an effective correction needs to be ‘mesh-informed’. A new two-scale framework is formulated to provide such correction: coupling between a local fine-mesh block (or a small number of local fine-mesh blocks) and a global coarse-mesh domain. This is achieved by harnessing the source terms arising from the imbalance when a finely resolved solution is projected to a coarse discrete space (under-resolved mesh), akin to the nonlinear product terms (‘Reynolds stresses’) in the time-averaged N-S equations. These ‘mesh-informed’ source terms updated on-the-fly enable mutual interactions between the local and global domains in a solution process.

Regarding the working of the two-scale method, one may wonder:what would the ‘mesh informed’ source terms notationally added for Resynolds-stress closure actually mean?The two-scale method has also been extended to solid conduction in solving a fluid-solid coupled conjugate heat transfer problem. The results of two-scale solid conduction solutions do provide a clearer ‘hint’ of the ‘mesh-informed’ source-term working. A solid-only setting having nothing to do with Reynolds stresses underlines the key role played by numerical discretization errors when a near-wall coarse-mesh is adopted (for cost-benefit) as in common WMLES (or WFLES). Because of the inherent numerical discretization errors in coarse-mesh nearwall flow solutions, it is argued that a correct Reynolds stress field (regardless of how it is obtained) may not produce a correct flow field. Nor is a correct wall-function (regardless of how it originates) expected to condition a coarse-mesh solution consistently leading to a correct flow field. Thus in such cases, should we take Reynolds-stress closure as the primary and sole target in the basic modelling formulations?

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