Introduction and scope of this site
The purpose of this site is to provide a resource for developers and users of wall-modeled large eddy simulation (WMLES). The site was created as an outcome of the “Workshop on the status and future directions of wall-modeled large eddy simulation for aeronautical applications” in Dec 2016, where a broad consensus was reached on the need for a repository of model descriptions and validation cases suitable for WMLES. The site is directly modeled on the Turbulence Modeling Resource at NASA Langley Research Center, which is aimed at RANS models.
The site is not aimed at being an online text book or review paper. There are several review papers on WMLES in the literature, including Piomelli and Balaras (2002), Piomelli (2008), and Larsson et al (2016). In addition, Spalart (2009) provides a review of DES (which can be used as a wall-model provided that the grid is sufficiently fine).
The site is aimed at being an easily accessible resource for anybody who wants to implement a wall-model in an existing LES code. To this end, descriptions of how to implement some common wall-models are provided for hybrid LES/RANS and wall-stress models. An equally important objective of this site is to be a resource for thorough verification/validation of wall-modeled LES. To this end, we provide grids, problem specifications, and reference data for multiple canonical test cases. We also provide results for these cases from some WMLES codes for comparisons.
Taxonomy of WMLES approaches
Wall-modeled LES is defined here as simulations in which the energetic scales of turbulence in the innermost 10-20% of the boundary layer are not resolved. The name “wall-modeling” is actually a misnomer: it is not the wall that is modeled, but rather the turbulence in the inner layer, and thus “near-wall-modeling” would be a better name. Nevertheless, the name “wall-modeling” has stuck in the community. There are two main approaches to WMLES:
- In hybrid LES/RANS approaches, a single grid that covers the full domain is used. The grid satisfies standard LES resolution requirements in the outer part of the boundary layer (the outermost 80-90%), but satisfies standard RANS resolution requirements in the inner part (i.e., the grid resolves the viscous length scale in the wall-normal direction but not in the wall-parallel directions).
- In the wall-stress modeling approach, the grid used in the LES solver covers the full domain. It satisfies standard LES resolution requirements in the outer part of the boundary layer (the outermost 80-90%), and a different set of requirements in the inner part of the boundary layer (to be discussed in more detail here). Since the LES grid does not resolve the energetic scales in the inner layer, an auxiliary wall-stress model is solved only over the inner layer. This wall-stress model takes the instantaneous LES velocity as the input and produces the instantaneous wall stress as the output; this is then fed back to the LES solver as a boundary condition.
All physics-based approaches to WMLES fall in either of the two broad classes described above. With “physics-based”, we mean an approach that recognizes that the equations become effectively averaged near the wall (each cell becomes larger than the energetic eddies) and thus that a model must become, at least to some degree, “RANS-like” near the wall. The vast majority of proposed WMLES approaches have been “physics-based” in this sense of the word.
In contrast, there have been a few (at most a handful) attempts at wall-modeled LES as a purely mathematical exercise, without appeals to physics, including the use of control theory by Nicoud et al (2001) (which presumes that the correct mean solution is known a priori) and the derivation based on filter properties by Bose and Moin (2014). These types of approaches are not covered on this site.