 Dobro. So, hello to everybody. I will speak on very applied simulation. So then the question to which I will address my talk is how to calculate the flow at very high Reynolds number with the access to the flow at subgrade scale. So, that's why I will talk about, I will speak about the LAES approach, but complemented with the stochastic subgrade acceleration model. So, and let me start with the famous washing machine experiment, where in between two contra-rotating disc, the light particle of polystyrene was emerged and then Nikolaj Mordang, Mikael Bourguan and all this team from Nikolaj Mordang, they observed the behavior of the particle. And what they've seen, it is real events of real violent velocity increment, for example here and one millimeter, almost one millimeter and there is 40 meters per second of velocity increment. And after, the particles follow with the constant velocity and then after again very huge acceleration and after light, the particle was grabbed by a demon and then withdrawn and then again grabbed and it was the signature of the life scale structure. So, and they calculated the acceleration distribution, they find the heavy tails in distribution of acceleration. Also, the rapid decorrelation of acceleration itself because of this change of the orientation and the long memory for the norm of acceleration. And so in the scenario was that the fluid particles is grabbed by the vertical structures and then it starts to rotate, rotate but conserving the norm following the structure. So, we need to simulate this flow. We know that there is no way to simulate it in Navias Tux equation since in application you have very high Reynolds number and at the same time, when you filter Navias Tux equation, the small scale discarded and so on, our concern is to combine LAS with subgrade scale model but accounting for the effect of intermittency and to find, you should choose the key variable for the subgrade model and the acceleration is the most appropriate variable because acceleration is the force per unit mass. And also if you applied the very classical estimations, the ratio of nonresolved acceleration towards the filtered one, then you see the path of nonresolved acceleration is growing with the Reynolds number. And so we decided to use the acceleration as a key variable since it depends on Reynolds number and it is more natural to construct the subgrade scale model on the acceleration. And these experimental results, that means that fast decorrelation on time of Kolmogorov's scale of the acceleration and the long memory for the acceleration itself can be represented by such a simple model and you see here the acceleration is relaxated by integral time while the velocity and while the acceleration is relaxated by Kolmogorov's scale and here there is the Vino 3D process so that means that direction and norm are weakly correlated here and then using ito calculus, you can easily come to this expression for the increment of the correlation between acceleration and velocity and then in stationary case, this is zero and Kolmogorov's scale is much less than integral scale and you come to the famous obok of diffusion coefficient in the space of velocity. So that means that all these despite the many papers and the new physics announced and so on and so on, in fact all these results confirm the Kolmogorov's obok of COD. So, and we proposed a few years ago, few years ago in 2011 then for Chernobyl 2013, 2011 also the approach LES double SAM and the idea very shortly I will remind the idea here is the instantaneous equation the continuity equation you decompose this Navier-Stokes equation on the filter path and fluctuating path this is the filter path this is the fluctuating path nothing new on the west then you should have the model no problem, the model exists since Magorinski you replace this nonlinear term by the Bucinesk approximation and this Magorinski form another equation is also cumbersome to result because we don't know neither fluctuating pressure neither fluctuation laplacio so another model is to replace, to replace this equation to replace this equation by this equation and I left the pressure gradient term to concern the solenoide solenoide dt and I introduced the stochastic model here ok, the acceleration here so the sum of this equation will no more our instantaneous equation before modeling the sum of those equations will represent the instantaneous equation of Navier-Stokes equation so now you addition these two equations you say that left hand side is the acceleration of some hypothetical flow field or reconstructive velocity field ok, then this is the pressure which satisfied this solenoide dt and the last, the last is to replace the filtered strain rate by the strain rate of this reconstructive velocity field the question is how to simulate the acceleration which comes from here so this is the model equation which we call stochastic Navier-Stokes equation as the sum of two proposals and it should be completed by the acceleration model on subgrid scale so since the experiment shows that direction of acceleration and amplitude they are weakly correlated then we consider two stochastic processes independently one for the norm and another for the orientation vector it's the unit vector which gives the orientation of acceleration for the norm of the acceleration we use the commagraph of 41 done in 61 obokov proposed the log normal conjection after the log normal conjection of commagraph in 1949 he proposed for the cold particles and then obokov proposed the log normal conjection for epsilon and then Pope proposed the stochastic equation for the epsilon from this log normal process and using eta transformation we could very easily to write the stochastic equation for the norm of acceleration it was used in the recent in the current LAS-WSAM approach and the direction was just sampled once from the Kalmogorov timescale so that means that real correlation be replaced by the stepwise function and so there are two shortcomings in this approach which poisoned us by our life the first one in fact for the box turbulence there is no supplementary dissipation on subrescale because the subrescale just accepts what's going on from the large scale and doesn't create another dissipation and when you calculate epsilon and this correlation which gives epsilon on subrescales it should be zero since the all the dissipation in the budget of the kinetic energy comes from here and it was not the case what not the case for the wall flow it may be because the dissipation can be created the acceleration can be created on very small scales closely to the wall so this is the first shortcoming and another shortcoming is that directed sample directly randomly at each Kalmogorov timescale it's not physically because there is no correlation between along the trajectory of particles so the naturally the idea comes to write the stochastic equation for the unit vector for the direction of the acceleration on the unit sphere this is the stochastic equation but if you multiplied by e and you will see that this equation conserved in norm of this time no problem but practically vina process is the explicit process and so practically it is very difficult to conserve the norm during the stochastic simulation for this equation it was our second challenge to do I will speak about this so the first proposal is to avoid the dissipation on subgrid scale we just replaced the modeled acceleration by its projection on the plate which is normal to the vector and so this tensor assures the projection from i to normal projection so then you see there is no more dissipation on subgrid scale the second proposal to write the Orsten-Olimbet process for the vector on unit sphere you write according to the definition of the increment of the velocity of the orientation of the acceleration you write in the framework of ito calculus the definition for components of this unit vector you show that if you calculate this the norm is conserved of the unit vector this is really very simple linear equation but to which process does it correspond and you can show going from strata knowledge to ito calculus that it comes to the Orsten-Olimbet a process in the ito calculus but you see it is nonlinear stochastic equation so that's why it will be very difficult to calculate by ito calculus this equation so we used this strata knowledge for this equation and we proposed the midpoint scheme there is a midpoint solution in the matrix form and then the second step you update this value by the implicit step calculating covariant elements determinant so now here you see the conservation of the amplitude of the orientation there is a correlation function the pdf is relaxing towards uniform distribution of the pdf of orientation and what are the results so first of all the statistics of fluid particles in the box turbines the evident result, the expected result the budget of the kinetic energy and this remark was given by Philips Palert and so on I'm happy now to reply to him that it is zero now you see it is zero second you see here the distribution of the probability, the stretched tails larger dissimulation comes up to here and doesn't present the tails and the boss model previously revisited of LAS-WSAM model gives those tails for the amplitude the pdf is also represented by the new model while LAS stops here and this is very important for example in combustion when you have high Reynolds number flow then your gradients at small scales can stretch the flamlet or to reignition for example in spray combustion the particles are of 5-10 microns and when particles evaporating particles is coming across such a violated border the vapor can be blocked up from the droplet the correlation here is a DNS here you see a short time and this was the goal of the simulation the revisited LAS-WSAM model is closely to DNS and then no difference between two models what is expected is very closely to the experiment if you see here the experiment is just here the correlation of the amplitude of the acceleration also the correlation time of order of integral time scale while here it is of order of commagor of time scale and here also at short time there is a correlation similar to that from DNS now about the statistics of inertial particles this is the classical Stokes equation for the particle dynamic UP is the velocity of particle UF is the velocity of flow and so here you can put either filter flow or LAS-WSAM or here so you see here the DNS in continuous line and empty symbol assemble it is LAS-WSAM and classical standard approach represent the field circle so we see that at low Stokes number the new approach gives the distribution with heavy tails in pdf of acceleration the same is the case in the correlation also there at short time they correlated with DNS and then they joined the standard LAS the same for correlation of the acceleration and so there is a hope that to apply it because it is really very simple to apply this approach to the industrial computation the access to the small scale structure which is depending on the local Reynolds number may be captured in the industrial computation Vainov, but still you have the constant in the Smagoniski closure how is important that constant? because this is something that the people didn't like anymore, the IBS so there is a constant that we don't want the constant we don't want the constant but then you are with the constant? no I think that if there is model better than Smagoniski it can be used here without any problem the additional trick to Smagoniski model it is to go inside to downward to small scale to subgrade scale and there I have no constant only because the local Reynolds number is the parameter and local Kolmogorov's acceleration is the parameter in those two definitions there are constant but classical ones there is no paradise in the life so you should calculate and see what is going on