Two-scale methods for LES/URANS

Conference item : Presentation

A common challenge in CFD simulations for both external and internal flows is in the near-wall region for wall-bounded turbulent flows. Fully wall-resolved LES (WRLES) solutions tend to be very costly particularly at realistically high Reynolds numbers, whilst wall-modeled LES (WMLES) are subject to considerable empiricism, further challenged by more recent findings on how outer flow large-scale coherent structures may influence inner near-wall flow small scales. The two-scale LES development is aimed at being much more affordable than WRLES and much less empirical than WMLES.

It must be noted that the cost benefit of WMLES 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’, and preferably can be enacted in-situ in a solution process. The 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 time-averaging flow equations. A space-time averaging is purposely introduced in either a direct or an inverse mode in the global domain and the local block respectively. The source terms in a compact form (one scalar for one flow equation) are directly obtained by simply taking the coarse-mesh residual using the space-time averaged fine-mesh solution. These ‘mesh-informed’ source terms updated on-the-fly enable mutual interactions between the local and global domain during a solution process. The converged solution for this two-scale coupled system should meet two seemingly conflicting requirements: an otherwise poorly conditioned local fine-mesh block is now subject to adequate environment/flow condition, and an otherwise poorly resolved global coarse-mesh domain is now effectively subject to high resolution.

In this lecture, the primary motivating considerations, the framework approach and the implementation methods will be presented and discussed. The validity and feasibility of the two-scale approach for efficient and accurate scale-resolving turbulent flow simulations will be illustrated in a range of cases of fundamental as well as practical interest.

Authors: He, L

• Publication status: Published
• Publisher: von Karman Institute for Fluid Dynamics
• Publication date: 2025-07-02
• Event title: Turbomachinery Flow Simulation and Modeling
• Event series: von Karman Institute Lecture Series
• Event location: Rhode-Saint-Genèse, Brussels, Belgium
• Event website: https://www.vki.ac.be/index.php/events-ls/lecture-series-events-2025/turbomachinery-flow-simulation-modeling-2025
• Event start date: 2025-06-30
• Event end date: 2025-07-04
• Language: English
• Subtype: Presentation