Abstract
Recent findings on wall-bounded turbulence have prompted a new impetus for modelling development to capture and resolve the Reynolds-number-dependent influence of outer flow on near-wall turbulence in terms of the ‘foot-printing’ of the large-scale coherent structures and the scale-interaction associated ‘modulation’. We develop a two-scale method to couple a locally embedded near-wall fine-mesh direct numerical simulation (DNS) block with a global coarser mesh domain. The influence of the large-scale structures on the local fine-mesh block is captured by a scale-dependent coarse–fine domain interface treatment. The coarse-mesh resolved disturbances are directly exchanged across the interface, while only the fine-mesh resolved fluctuations around the coarse-mesh resolved variables are subject to periodic conditions in the streamwise and spanwise directions. The global near-wall coarse-mesh region outside the local fine-mesh block is governed by the augmented flow governing equations with forcing source terms generated by upscaling the space–time-averaged fine-mesh solution. The validity and effectiveness of the method are examined for canonical incompressible channel flows at several Reynolds numbers. The mean statistics and energy spectra are in good agreement with the corresponding full DNS data. The results clearly illustrate the ‘foot-printing’ and ‘modulation’ in the local fine-mesh block. Noteworthy also is that neither spectral-gap nor scale-separation is assumed, and a smooth overlap between the global-domain and the local-domain energy spectra is observed. It is shown that the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for the conventional fully wall-resolved large-eddy simulation (LES) to $O(Re)$ for the present locally embedded two-scale LES.
Highlights
Numerical solutions of turbulent flows have been challenging especially under a high-Reynolds-number condition, closely relevant to practical applications in many fields
We develop a two-scale method with a locally embedded fine-mesh block generated by sub-dividing the base coarse mesh cells in the near-wall region
2013) and the streamwise and spanwise sizes are taken based on the spatial spectra of the full direct numerical simulation (DNS) data (Lee & Moser 2015) to ensure sufficient coverage of the resolved
Summary
Numerical solutions of turbulent flows have been challenging especially under a high-Reynolds-number condition, closely relevant to practical applications in many fields. Pascarelli, Piomelli & Candler (2000) developed a method to couple a global coarse-mesh outer flow domain with a local small fine-mesh near-wall block (often labelled as a ‘minimum flow unit’ (MFU) with direct periodic conditions in the two wall-parallel directions). A common key limitation suffered by those previous local-domain-based methods seems to arise from the use of a near-wall MFU subject to the spatial periodic conditions, inherently impeding the ‘foot-printing’ by large-scale turbulence structures in an outer flow region. It is intended that the global coarse-mesh should sufficiently capture and resolve all large-scale turbulence structures, while the near-wall local fine-mesh block is designed to capture both the basic ‘universal’ self-sustaining dynamics and the ‘foot-printing’ of the large scales. Domain configuration for the channel flow with locally embedded block
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