“…the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by small eddies and large” – Leonardo di ser Piero da Vinci
Being so passionate for the subject of turbulence modelling I shall kick off with my favorite, SGS… 😉
LES SGS Modelling
As explained in the exposition, in LES the large energetic scales are resolved while the effect of the small unresolved scales is modeled using a subgrid-scale (SGS) model and tuned for the generally universal character of these scales. This is usually done by a spatially filtering the NSE with some kind of shape filter (may it be cutoff, top hat, etc…). The most common representation, is a linear stress-strain relation relying on the Boussinesq hypothesis and the eddy viscosity concept. The first and possibly still the most popular is the Smagorinsky model. Applying the Smagorinsky model to flows other than those it was tuned for, shall prove out of its range of applicability consequence of its many shortcomings, fully explained in my former post That’s a Big W(H)ALE as well as the remedies to overcome these shortcomings from a purely physical perspective.
Models such as these are termed “explicit SGS Models” as the filter and its shape are “clearly” defined (Its effect not quite though…). Other popular explicit modelling procedures include:
- Dynamic models (Going Dynamic I )
- Scale similar and mixed models (Bardina et al.)
- Structure function models (Lesieur – great book by the way, very recommended)
- Deconvolution methods (Stoltz et al.)
Another route for modelling the effect of unresolved scales is found through the utilization of higher order numerical schemes to take the role of the explicit filter in the aim of adding dissipation only in the high wave number range (small and unresolved scales) – termed Implicit LES (ILES). The first of such method was MILES (F. Grinshtein, also followed by a good book on the subject of ILES).
There is an option to combine both implicit and explicit LES. Although seemingly reasonable, there is a high potential for numerical contamination near the filter cutoff range due the reciprocity of the methods when applied as one scheme and of course the problem of separating the effect on dissipation of a specific spatial numerical scheme from that of the explicit filter (especially for non-canonical cases). Personally I am not aware of successful validated models combining classical implicit-explicit modeling.
Saying all that the problem of computing resources in near wall LES may shift the attention for methods such as WMLES DDES/DES as explained in my former post: Detached Eddy Simulation – an attractive methodology to RANS in the aid of LES
Every LES practitioner knows that one of the most important tasks conducting LES is applying correct inflow conditions. If the flow in the numerical domain is purely turbulent, a complete LES must account for turbulent structures in the flow at the inflow region.
There are some cases where one choice or another of inflow conditions might have a minimal effect on the description of a specific phenomena (e.g. extremely massive separation), but generally the effect of best applying inflow conditions could mean the difference between seemingly colorful albeit worthless unsteadiness cartoon and CFD.
Among the most popular methods for the generation of inflow conditions is to introduce an artificial perturbation (based on Fourier series for example) to the mean flow.
There are two subtleties in the method. First, the perturbation must be tuned such that it is high enough to produce turbulence, but not too high as to produce crazy unphysical results. The second is that the numerical domain has to be built such that the perturbation shall have enough downstream evolving space.
Another method is to extract dependent variables downstream to the inflow, rescale them and dynamically apply them to the inflow boundary, this way the introduction of inflow conditions is generated implicitly in the simulation itself. The main shortcoming of the method is that special care must be taken to the actual rescaling process.
An interesting method considers tripping the inflow region itself using blowing and suction at the inflow. Such operations may generate bypass transition through generation of high levels of turbulence in the free stream, a mechanism dominated by diffusion effects as turbulence is diffused into the boundary layer from high free stream levels (short in-depth description of the mechanism from former post: A Forest of Hairpins – on the quest for turbulence coherent structures )
Outflow and other Computational Boundaries
The consideration of other boundaries except of the obvious inflow conditions is extremely important for aeroacoustic applications, subsonic flows and reacting flows, where unphysical numerical reflections from the boundary may totally contaminate the results.
Popular methods for the treatment of boundary conditions for such purposes are the use of gradually increasing grid spacing in combination with dissipation of the numerical method at hand in order to damp waves near the boundary.
Some other methods use characteristic wave relations to eliminate the effect.
Another method is to deliberately include source terms in the equations themselves to increase damping of specific features that are major contributors for such a reflective behavior from the computational boundaries.
If the simulation allows it, generally when there is a dominant homogenous direction, periodic conditions could be applied. In such a case the domain must be large enough (upstream-downstream) as to relaxing unwanted downstream features.
Handling initial transients in an LES
As LES promotes unsteadiness, solutions must run a period long enough for achieving an “equilibrium” turbulent state as the transients effect evolves well and disappear from the simulation. especially considering low Mach number simulations, the process shall take a long time but is essentially crucial in order for those transients to not corrupt statistical quantities and temporal averages. This of course translates directly to excessive use of computational resources. One way to overcome some of the difficulties and speed-up the process is using a solution from a previous RANS simulation. such a procedure is presented in the DESider Project .
Don’t miss LET’s LES III…