It’s quite amazing how Computational Fluid Dynamics (CFD) progress has been tremendous in the past half a decade.

Moore’s Law vision of an exponential growth in computational resources lived up to its expectation and it’s by many predicted to keep doing so for the next 20 years if not more.

*Moore’s Law applied to CFD*

One huge leap forward was achieved through the ability to simulate Navier-Stokes Methods Such as *Reynolds-Averged Navier-Stokes (RANS)*.

RANS is based on the Reynolds decomposition according to which a flow variable is decomposed into mean and fluctuating quantities. When the decomposition is applied to Navier-Stokes equation an extra term known as the *Reynolds Stress Tensor *arises and a modelling methodology is needed to close the equations. The “closure problem” is apparent as higher and higher moments of the set of equations may be taken, more unknown terms arise and the number of equations never suffices.

Reynolds-Stress Tensor

Levels of RANS turbulence modelling are related to the number of differential equations added to Reynolds Averaged Navier-Stokes equations in order to *“close” *them.

1-equation and 2-equations models, incorporate a differential transport equation for the turbulent velocity scale (or the related the turbulent kinetic energy) and in the case of 2-equation models another transport equation for the length scale, subsequently invoking the* “Boussinesq Hypothesis”* relating an *eddy-viscosity* analog to its kinetic gasses theory derived counterpart (albeit flow dependent and not a flow property) and relating it to the Reynolds stress through the mean strain.

# Scale-Resolving Simulations (SRS)

Two main reasons for using SRS models should generally be mentioned.

The first is for applications of which additional information that cannot be obtained from the RANS simulation is needed such as aeroacoustics applications where turbulence generated noise that can’t be extracted from RANS simulations with sufficient accuracy, material failure applications governed by unsteady mixing zones of flow streams at different temperatures dependent on unsteady heat loading, applications regarding vortex cavitation caused by unsteady turbulence pressure fields, calculation of helicopter loads which are strongly dependent on the vortices generated by the tip of the rotor and alike. SRS might be mandatory in such situations even in cases where the RANS model can indeed compute the correct time-averaged flow field.

The second reason for using SRS models is related to the fact that although RANS methodology strength has proven itself for wall bounded attached flows due to calibration according to the “law-of-the-wall”, for free shear flows, especially those featuring a high level of unsteadiness and massive separation it has shown poor performance following inherent limitations as a one-point closure that does not incorporate the effect of strong non-local effects and of long correlation distances characterizing many types of flows of engineering importance.

Considering that RANS models typically already have limitations covering the most basic self-similar free shear flows with one set of constants, there is little hope that even advanced Reynolds Stress Models (RSM) methodologies will eventually be able to provide a reliable foundation for all such flows.

## Second Generation URANS – SAS and PANS – An Alternative to LES:

### Scale Adaptive Simulation (ANSYS Menter and Egorov)

An interesting methodology to simulate Large-Eddy Simulation (LES) like unsteadiness, lies in the midst of RANS and LES and is especially attractive for flows of which strong instabilities of the flow exist, is termed *Scale Adaptive Simulation (SAS)* (Menter and Egorov, also available in the Fluent code).

*k-w SST Vs. SAS*

In SAS formulation, two additional transport equations are solved for. The first is the turbulence kinetic energy transport equation (k) and the second for the square root of KL transport equation (hence the name kskl turbulence model).

What distinguishes the KSKL model from other 2-equation closures is the fact that in the last, the turbulence length scale (which may be defined on dimensional grounds by the transported variables) will always approach the thickness of the shear layer, while for KSKL model, the behavior is such that it allows the identification of the turbulent scales from the source terms of the KSKL model to a measure of both the thickness of the shear layer but also for non-homogenous conditions, as the Von-Karman length scale is related to the strain-rate, individual vortices have locally different time constants (inversely to turnover frequencies) and therefore from a certain size dependable upon the local strain rate, they may not be merged to a larger vortex.

Meaning that the Von-Karman length scale gives a first order estimation for the spatial variation.

SST-URANS Vs. SAS – Circular cylinder in a cross flow at Re=3.6⋅106

( Iso-surface of Q=S2-Ω2, coloured according to the eddy viscosity ratio).

### The Partially-Averaged Navier-Stokes (PANS) Method

In PANS method, the so-called “partial averaging” concept is invoked, which corresponds

to a filtering operation for a portion of the fluctuating scales. This concept is based on the observation that the optimum *resolved-to-modeled ratio *will change from one engineering application to another depending on the reciprocal relations between the level of physical fidelity intended, geometry at hand and computational resources available.

The most important feature which is in the foundation of the approach is the *averaging-invariance property* of Navier-Stokes equation which amounts to the fact that for any resolved-to-modeled ratio achieved by filtering (i.e. partial filtering), the *sub-filter scale stress* has the same characteristics as the Reynolds stress,** therefore similar closure strategies as for RANS may be employed**.

This is a very attractive feature since RANS closure strategies are very mature and well-tested as RANS has truly been the work horse for most large-scale engineering applications, in contrast with LES closures which are mostly algebraic and suffer from lack of complex engineering applications validity.

The original PANS model is therefore based on the 2-equation RANS modelling concept and solves two evolution equations for the *unresolved kinetic energy and dissipation*.

*LES Vs. PANS*

It is widely known and goes all the way back to Richardson and granted a more precise view by Kolmogorov, that in turbulence physics, large scales contain most of the kinetic energy and much of the dissipation occurs in the smallest scales, **The smaller the unresolved kinetic energy is, the smaller is the modeled-to-resolved ratio and the greater are both computational effort and physical fidelity for a suited numerical resolution. moreover, the highest value that could be attained for the unresolved dissipation implies that RANS and PANS unresolved scales are the same.**

The end result for the evolution equations (different coefficients and parameters definitions may be found at S. Girimaji 2005)

The PANS methodology might theoretically hold the following very attractive features:

- The PANS methodology is based on the kinetic energy content and the RANS 2-equation closure methodology rather than on a grid-dependent filter, rendering the model as closed in contrast to LES which is essentially an unclosed method.

Perhaps new advances on the route to “grid-independent” LES modelling (S. Pope, U. Piomelli) shall resolve some of the issues but it shall take some time before such methodologies shall find their way to general purpose CFD codes as most of the exploit dynamic LES non-local concepts. - As the sub-grid scale filter is independent on the grid resolution explicitly but on the unresolved kinetic energy and dissipation there is a decoupling between the physical and numerical resolution.
- The two evolving parameters unresolved kinetic energy and dissipation may be either constant (as a fraction of RANS) or spatial and time dependent (such as in DES) rendering PANS as more of an infrastructure for resolved-scale simulation rather than a simple modelling approach.

The original PANS model is based on the 2-equation RANS modelling concept and solves two evolution equations for the *unresolved kinetic energy and dissipation*.

It is widely known and goes all the way back to Richardson and granted a more precise view by Kolmogorov, that in turbulence physics, large scales contain most of the kinetic energy and much of the dissipation occurs in the smallest scales, The smaller the unresolved kinetic energy is, the smaller is the modeled-to-resolved ratio and the greater are both computational effort and physical fidelity for a suited numerical resolution. moreover, the highest value that could be attained for the unresolved dissipation implies that RANS and PANS unresolved scales are the same.

## Direct Numerical Simulation (DNS)

My first actual encounter with DNS was while researching for my thesis relating to the role of hairpins in transition and turbulence (specifically originating from bypass transition mechanism). ChannelFlow code as simple as it was made me feel ever so powerful in my direct confrontation with turbulence… 😉

Turbulence phenomena is very precisely described by a seemingly simple set of equations, the Navier-Stokes equations, their nature is such that analytic solutions to even the most simple turbulent flows can not be obtained and resorting to numerical solutions seems like the only hope.

But the resourcefulness of the plea to a direct numerical description of the equations is a mixed blessing as it seems the availability of such a description is directly matched to the power of a dimensionless number reflecting on how well momentum is diffused relative to the flow velocity (in the cross-stream direction) and on the thickness of a boundary layer relative to the body – The *Reynolds Number.
*It is found that the computational effort in Direct Numerical Simulation (DNS) of the Navier-Stokes equations rises as Reynolds number in the power of 9/4 which renders such calculations as prohibitive for most engineering applications of practical interest and it shall remain so for the foreseeable future, its use confined to simple geometries and a limited range of Reynolds numbers in the aim of supplying significant insight into turbulence physics that can not be attained in the laboratory.

*Turbulent Boundary Layer (P. Schlatter and D. Henningson of KTH)*

Saying all that, it is not expected that DNS will take on vital role in the engineering design process, where many designs are to be evaluated working through a repetitive cycle of obtaining a CAD geometry–> grid generation–>Solving the equation–>post-processing the results–>optimization decisions.

Nonetheless, DNS shall find its place in the industrial CFD community for specialized research as it does in the academy, where on the line of an academic study which lasts up to approximately 5 years only a few high-fidelity simulations are conducted

The above presents a three dimensional direct numerical simulation using high-order methods has been performed to study the flow around the asymmetric NACA-4412 wing at a moderate chord Reynolds number (Rec = 400,000), with an angle of attack of 5 degrees. This flow regime corresponds approximately to the flow around a small glider. In addition to providing highly accurate data, high-order methods produce massive amount of data enabling proper flow visualization. For instance, in this study vortical structures emerging from tripping the flow to turbulence are visualized using the lambda2 criterion. It is interesting to see how interaction of such vortical structures from the turbulent boundary layer and the turbulent wake creates a natural art of its own.

## Large-Eddy Simulation (LES)

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. LES has severe limitations in the near wall regions, as the computational effort required to reliably model the innermost portion of the boundary layer (sometimes constituting more than 90% of the mesh) where turbulence length scale becomes very small is far from the resources available to the industry. Anecdotally, best estimates speculate that a full LES simulation for a complete airborne vehicle at a reasonably high Reynolds number will not be possible until approximately 2050…

Modeling of LES is formally described by the application of spatially filtering NSE. An explicit approach would explicitly apply a filter with some kind of shape (may it be cutoff, top hat, etc…). subsequently, a model is devised to capture the effect of under-resolved length-scales. 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
- 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).

## Hybrid RANS-LES

As LES shall remain too expensive in the following few decades for the ever increasing number of engineering complexities (e.g. complete aircraft wing), researchers have shifted much of the attention and effort to hybrid formulations incorporating RANS and LES in certain ways. Due to the fact that computational cost of LES is practically independent on the Reynolds number for free shear ﬂows, only weakly dependent on the Reynolds number for the outer portion of the turbulent boundary layer, but becomes strongly dependent on the Reynolds number for the innermost layer (the viscous sublayer, the buffer layer and the initial part of the log layer), in most hybrid RANS-LES methods RANS is applied for an inner portion of the boundary layer and large eddies are resolved away from these regions by an LES (e.g. WMLES).

*Detached Eddy Simulation (DES)*

One of the most popular hybrid RANS-LES models is Detached Eddy Simulation (DES) devised originally by Philippe Spalart. The term DES is based on the Idea of covering the boundary layer by RANS model and switching the model to LES mode in detached regions thereby cutting the computational cost significantly yet still offering some of the advantages of an LES method in separated regions.

The formulation of the hybridization of the model is fairly straight forward:

This means that as Δ is max(ΔX, ΔY, ΔZ) this modification of the S-A model, changes the interpretation of the model as the modified distance function causes the model to behave as a RANS model in regions close to walls, and as an eddy-viscosity based LES (Smagorinsky, WALE, etc’…) manner away from the walls.

The original DES is set to Spalart-Allmaras eddy-viscosity transport equation to achieve an eddy viscosity (see the link for an in-depth evaluation of the turbulence model) for RANS mode and an eddy-viscosity based LES model (such as WALE for example).

The actual formulation for a two-equation model is (the turbulence kinetic energy equation of a k-ω model):

In subsequent improvements to the DDES formulation, RANS are applied to the **innermost** portion of the boundary layer and large eddies are resolved away from these regions. In such formulation LES is confined to the rest of the boundary layer or to regions where flow is detached which provides a Wall-Modelled Large-Eddy Simulation (WMLES) of attached flows at high but fair computational cost.

*Improved-DDES for the flow behind a circular cylinder*

Another subtlety concerns that concerns the “grey area”, specifically the region of transition between RANS and LES models. DES utilizes a model parameter very similar to the one in Smagorinsky LES model which is found deficient in the ability to handle laminar-turbulent transition (among other deficiencies). The same is observed in DES as high levels of eddy viscosity attenuate the transition process which contribute to the **“grey area” problem**, specifically the RANS to LES transition by interfering with “turbulence content” arising from shear layer instability. This is an ongoing issue with DES and some options to overcome this “grey area” phenomena incorporating local formulation (so as they can be straightforwardly implemented in an OpenFOAM code) have been proposed such as processing the local velocity gradient to distinguish between situations of which the eddy viscosity is low (such as plane shear) to regular turbulence, where the subgrid-scale model of the LES can be in use.

### Grid Induced Separation

Being so popular, some of the natural DES (P. Spalart 1997) inherent limitations were often overlooked in simulations as practitioners often apply the model in order to increase physics fidelity without dwelling on subtle issues. The following paragraphs address some of these subtleties (following references from P. Spalart et al. 2006 and F. R. Menter 2000).

In DES the hybrid formulation has a limiter switching from RANS to LES as the grid is reduced. The problem with natural DES is that an incorrect behavior may be encountered for flows with thick boundary layers or shallow separations. It was found that when the stream-wise grid spacing becomes less than the boundary layer thickness the grid may be fine enough for the DES length scale to switch the DES to its LES mode without proper “LES content”, i.e. resolved stresses are too weak (“Modeled Stress Depletion” or MSD”), which in turn shall reduce the skin friction and by that may cause early separation. The phenomenon is termed Grid Induced Separation (GIS).

*mean velocity in different types of grids in a boundary layer – *

*top: natural DES, left: ambiguous grid spacing, right: LES*

As a consequence of the original DES deficiencies an advancement to the model was devised, termed Delayed-DES (DDES). In the Fluent DES-SST formulation a DES limiter “shield” is added to maintain RANS behavior in the boundary layer without grid dependency.

### Delayed Detached-Eddy Simulation (DDES) Formulation

The main corner stone for the DDES hybrid RANS-LES model is the Spalart-Allmaras Turbulence Model. One transport equations for the eddy-viscosity based models such as Spalart-Allmaras don’t have an internal length scale as far as a measure of the mean shear rate is concerned, but do incorporate a ratio (squared) of a model length scale to the wall distance. The parameter is modified in the DDES formulation to support any eddy viscosity based model (a straightforward procedure to extract an eddy viscosity transport model from a two transport equations model )

where νt is the kinematic eddy viscosity, ν the molecular viscosity, Ui,j the velocity gradients, κ the Kármán constant and d the distance to the wall.

As the length scale is 1 in the logarithmic layer and gradually goes to zero in the boundary layer edge the kinematic viscosity is added to the formulation to ensure its stays correct in high proximity to the wall such that the length scale remains away from zero (exceeding 1).

A function is defined to ensure that the solution will be a RANS solution even if the grid spacing is smaller than the boundary layer thickness (so it will be 1 in the LES region where the length scale defined above is much smaller than 1, and 0 elsewhere while not sensitive in situations of high proximity to the wall when the length scale exceeds 1.

Now an alteration to the DES length scale is proposed such that under specific coefficient values (which the above function is not so sensitive to even in the case of a different formulation of DES other than spalart-Allmaras, say the k-ω SST Model – we shall see such a formulation shortly)

In this formulation, when the function is 0, the length scale dictates RANS mode to operate, and when the function is 1 natural DES (P. Spalart 1997) applies. The difference lies in the fact that on contrary to natural DES formulation where the length scale depends solely on the grid, in the DDES formulation it depends also on the eddy-viscosity. This means that the revised formulation will “insists” upon remaining on RANS mode if the grid is inside the boundary layer and if massive separation is encountered, the functions value will switch to LES mode a much more abrupt manner than the switch in the natural DES formulation, rendering the “grey area” narrower which is highly desirable.

The original DDES is set to Spalart-Allmaras eddy-viscosity transport equation to achieve an eddy viscosity (see the link for an in-depth evaluation of the turbulence model) for RANS mode and an eddy-viscosity based LES model (such as WALE for example).

*Vorticity isosurfaces in a circular cylinder simulation (F. Spalart 2009)*

For two-equation models, the dissipation term in the turbulence kinetic energy equation is formulated as follows:

It is worth mentioning that DES and its variants are termed and essentially are *global hybrid methods.
*Global hybrid methods are based on a continuous treatment of the flow variables at the interface between RANS and LES and by that introduce a ‘grey area’ in which the solution is neither pure RANS nor pure LES since the switch from RANS to LES does not imply an instantaneous change in the resolution level. These methods can be considered as weak RANS–LES coupling methods since there is no mechanism to transfer the modelled turbulence energy into resolved turbulence energy.

In the above formulation The function FDDES is designed as to reach unity inside the wall boundary layer and zero away from the wall. The definition of this function is intricate as it involves a balance between proper shielding and not suppressing the formation of resolved turbulence as the flow separates from the wall. As the function FDDES blends over to the LES formulation near the boundary layer edge, no perfect shielding can be achieved. The limit for DDES is typically in the range of the maximum edge length of the local computational cell is less then 20% of the boundary layer thickness which allows for meshes where the maximum edge length of the local computational cell is of 20% than for natural DES. However, even this limit

is frequently reached so the GIS phenomena is not fully prevented with DDES.

There are a number of DDES models available in ANSYS Fluent/CFX. They follow the same principal idea with respect to switching between RANS and LES mode. The models differ therefore mostly by their RANS capabilities and should be selected accordingly.

### Shielded Detached Eddy Simulation (SDES)

The SDES formulation is yet another variation of DES. The improvement is in the shielding function and the interaction with the grid scale. This is emphasized in the turbulence model by an additional sink term in the turbulence kinetic energy equation:

The shielding function in the SDES formulation (namely – fs) provides more shielding then the corresponding shielding function in the DDES formulation (F-DDES), this means that the original shielding based on the mesh length scale can be reduced and is therefore defined in SDES as:

The first part in the above is the conventional LES mesh length scale, the second is again based on the maximum edge length as in the DES formulation and the 0.2 in the above ensures that for highly stretched meshes the grid length scale is a fifth of that of DDES and another implication is the reduction of the eddy-viscosity in LES mode by a factor of 25 as it is dependent quadratically upon the grid size. This is an important artifact as it improves the RANS to LES transition of DES models.

In engineering flows, flow characteristics of shear flows is much more encountered than that of decaying isotropic turbulence (DIT). The last is the basis for the calibration of the DES/DDES constant. Shear flows the Smagorinsky constant is reduced and this is achieved by setting the constant in SDES to 0.4.

Now if we combine the above explained effect of the grid scale on the eddy viscosity with the modified constant a reduction by a factor of nearly 60 is achieved for separated flows on stretched grids which is favorably affects the RANS to LES transition.

### Stress-Blended Eddy Simulation (SBES)

SBES is not a new hybrid RANS-LES model, but a modular approach to blend existing models to achieve optimal performance. In this sense SBES is a modular approach which allows the CFD practitioner to use a pre-selected RANS and another pre-selected LES model instead of the mix of both formulations within one set of equations.

This becomes handy in certain fields of which the modeling sophistication is to be extended from what was originally practiced with a specific and validated LES to include parts of the domain which can only be covered by RANS models without having to replace the trusted LES.

SBES model concept is built on the SDES formulation. In addition, SBES is using the shielding function to explicitly switch between different turbulence model formulations in RANS and LES mode.

For the general case one of the (RANS or LES) models is not based on the eddy viscosity concept the general formulation is presented either in modeled stress tensor:

For the case where both RANS and LES models are based on the eddy viscosity concepts, the formulation simplifies to:

The strong shielding is important for such a formulation to work in order to maintain a zero pressure gradient RANS boundary layer in any grid.

The intention of the SBES methodology is to resolve the following issues (F. R. Menter 2016):

- Exhibit an asymptotic shielding of the RANS boundary layers.
- perform an explicit switch to user-specified LES model in LES region.
- Allowance of rapid ‘transition’ from RANS to LES regions Allow practitioners to be able to clearly distinguish regions where the models run in RANS and regions where the model runs in LES mode.
- Allow Wall-modeled LES capability once in regions of sufficient numerical resolution and an upstream trigger into LES-mode for WMLES simulations.

**Summing up all of the above, the following SRS models are available in the ANSYS CFD codes:**

- Scale-Adaptive Simulation (SAS) models:

a. SAS-SST model (Fluent, CFX) - Detached Eddy Simulation (DES) Models:

a. DES-SA (DDES) model (Fluent)

b. DES-SST (DDES) model (Fluent, CFX)

c. Realizable k-ε-DES model (Fluent) - Shielded Detached Eddy Simulation (SDES):

a. All ω-equation based 2-equation models in Fluent and CFX. - Stress-Blended Eddy Simulation (SBES):

a. All ω-equation based 2-equation models in Fluent and CFX. - Large Eddy Simulation (LES):

a. Smagorinsky-Lilly model (+dynamic) (Fluent, CFX)

b. WALE model (Fluent, CFX)

c. Kinetic energy subgrid model dynamic (Fluent)

d. Algebraic Wall Modeled LES (WMLES) (Fluent, CFX) - Embedded LES (ELES) model:

a. Combination of all RANS models with all non-dynamic LES models (Fluent)

b. Zonal forcing model (CFX)

## The incorporation of SRS in engineering process

In order for SRS to be best incorporated in engineering design process there are some challenges to overcome, most of which are related to LES rather than second generation URANS, based on RANS methodology which is very mature and well-tested as RANS has truly been the work horse for most large-scale engineering applications, in contrast with LES closures which are mostly algebraic and suffer from lack of complex engineering applications validity.

### Optimization and sensitivity analysis

Engineering design process is based on an iterative design achieving the best product through assessing a current design by optimization methodologies such as *local sensitivity analysis*, by which gradients of design parameters are calculated subsequently to be employed in gradient-based optimization algorithms.

In order to being able to use LES in such quantifications of design parameters it needs to be incorporated with tools of sensitivity analysis to measure how uncertainty factors affect the performance of the design.

The problem is that LES is a non-linear dynamical system, hence suffers from chaotic behavior. Local calculations of quantities of interest of which initial conditions slightly depart, exponentially diverge as time advances. A robust methodology to avoid uncertainty calculations divergence is mandatory if LES is to participate in the engineering design process.

*The “strange attractor” – chaos and fractals (Lorenz)*

*Geometry, grid generation and numerical schemes*

In order for LES to come forth on its future vital role, many adjustments and advancements to current dominating LES approaches should be conducted. In essence, what differs practical engineering applications from their academic counterparts is the level of geometry complexity. Unstructured meshing for complex geometries has been dominating industrial CFD and from an LES standpoint this means that large errors due to commutation of non-commutative operations may hamper results accuracy substantially.

Advancements of Immersed Boundary Method (IBM), in which the boundaries of the body do not conform to the grid, the governing equations are discretized on fixed meshes and applying boundary conditions requires modifying the equations in the vicinity of the solid boundary by means of a forcing function that reproduces the effect of the boundary, are promising as far of high fidelity simulations of complex geometry and especially for moving meshes are concerned.

*A snapshot of Large Eddy Simulation of a 5-bladed
rotor wake in hover with a novel multiblock IBM
*

*(by Technion CFD Lab – S. Frankel)*

Some new advancements in mixed-models (such dynamic and Smagorinsky) based on the integral formulation of the LES equation (F. M. Denaro) alleviate some of commutation problematic issues and allow for a much more accurate filtering.

Moreover, of true importance is the increasing the level of automation. As HPC shall keep obeying Moore’s law in its advancement, CFD workflows shall suffer tremendously from the “human-in-the-loop” syndrome, where the practitioner is too much involved, especially in the geometry accommodation and grid generation phases of the design and analysis.

Adaptive grid-generation for SRS are also a challenge. While in RANS grid adaptation is aimed only on reducing numerical error, for LES it is intended also to improve SGS model errors and increase the fraction of resolved motions. Suggestions to alleviate the difficulty are strongly related to the fact that standard algebraic eddy-viscosity modeling approach render LES as unclosed in the sense that the filter to be applied is not grid-independent. One exciting route of such by SB Pope suggesting adaptation aiming on resolving a user-deﬁned fraction of the kinetic energy, and also presented an incorporation of such in dynamic modeling.

### High Power Computing (HPC)

The effectiveness and impact of CFD on the engineering design process is extremely dependent on the power and availability of modern HPC systems. During the last decades, CFD codes were formulated using message passing (MPI) software models which match nowadays parallelism efficiently. As future route and prevailing computing hardware, memory architecture (hierarchical not supported by MPI) and network connecting is not a-priori known new algorithms have to be supportive and advance hand to hand with computing resources.

Numerical schemes such must also support tremendous parallelism in future exascale computing. Schemes involving global operations shall not prevail do to obvious bottlenecking.

*Worldwide top HPC and its utilization*

The second issue relates to the fact that in order to utilize such computational advancements, methodologies for SRS should be developed as to be also used outside the academy. As much as it is important that novel modelling techniques shall be validated and tested on simple canonical problems (e.g. ZPGBL/couette/channel/pipe flows) which lend themselves to detailed assessment, they should be developed to be also applied to real engineering problems.

It is no coincidence that the k-ω SST 2-equation turbulence model (F. Menter) Detached-Eddy Simulation (DES) (P. Spalart) and WALE LES model (F. Nicoud and F. Ducros) have gained such popularity. It is the fact that each of them was devised intentionally to perform well for industrial applications, that made them such. A good example is non-local operations which find their way to many LES formulations. Their use in commercial CFD code environment is near to impossible.

The computational time can be estimated if we assume that the turbulent Reynolds number is proportional to the mean flow Reynolds number Rt = ζ Re, where ζ is an empirical coefficient usually close to 1/10 in confined flows (and in usual Reynolds numbers range). It is then proportional to the Reynolds number according to the law t ∝ 64ζ Rt 11/4 . These numerical order of magnitudes clearly show that DNS (or even highly resolved LES) implies a huge numerical task and still remains difficult to reach in practice at the present time even if considering the Moore’s law suggesting that the number of transistors of a processor doubles every second years (10 years = factor 32) and of top nowadays supercomputers :

## Democratization of SRS

I read quite an interesting post (by Keith Hanna – Mentor Graphics) about the “Democratization of CFD“. Referring to SRS, it is quite obvious that in order for LES to be widespread in the design process, it clearly needs to be much more accessible to non-proficient practitioners. In my post “Let’s LES” I have reviewed some of LES mandatory set of tools without which the credibility of the simulation is doubtful at best. When a non-proficient practitioner tries to perform an LES, there are many instances of which being able to construct an animation of a time-varying flow that looks like a turbulent flow seems very satisfying. However, this offers no guarantee that the appropriate grid resolution has been used, spatial and temporal schemes have been selected, boundary conditions (especially time-varying, turbulent containing inflow conditions) are proper, etc’… CFD practitioners have to be educated to control a much different set of tools than those they were used to with RANS (and other low fidelity methodologies) to actually achieve the added benefit that LES could provide.

### So to conclude…

even though it’s safe to predict that SRS (and especially LES) shall not replace RANS in the near future, the level of physical fidelity achieved by SRS shall have a growing impact on engineering design process.

Returning to Moore’s law prediction it could be assumed that LES is going to take more and more of a vital role in engineering design process, being ever so attractive as its level of fidelity is such that it combines the advantages of simulations along with reliability features of experiments. This allows the engineer to build up his confidence while extracting high fidelity realizable results, such that the margin of safety could be tightening for the few more percentages of optimality which are the hardest to achieve.

For this forecast to become reality, the one conclusion shared by most authors was that sincere confrontation with SRS challenges should be conducted while also taking under consideration its practicality to engineering design process.

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