Title of the Blog + LB SGS model, MD SGS model, or Schrödinger SGS model + Hardware-CFD-devices(CFD FPGA) …

I have been asked many times whether I mean I completely disagree with the Navier-Stokes equations. The response is absolutely, NO. The title of this Blog is just a title, i.e. a controversial title. What I mean is that N-S is not completely reproducible of all physical phenomena occurring in fluid flow at different flow regimes.

As for turbulence, as many ones believe, of course if it was computational feasible, the best model would be to just consider fluid molecules and then all what we need to take into account is most probably only the intermolecular forces. But we all know that it may not be possible even by next century unless a revolution happen in quantum computers and quantum information technologies.

So, what are choices? Keep continuing dealing with N-S, averaging, playing mathematically (manipulating) and sometimes physically the models, collecting experimental data and fits into new turbulence models, …?

These have been done for decades and so far no fundamental progress. Many ones believe that there has been no fundamental progress since Kolmogorov. However, to me DNS and LES also have been giant steps but limited to the existing assumptions and understandings.

Here there are 2 main questions: 1) what to do toward better physical understanding and more accurate models 2) how to search for better numerical tools.

As for the latter, I would say, the applied mathematician are doing their jobs nicely; of course not very quickly because of funding issues, lack of public interests among students to get into the applied-math-world and so on.

But for the former, to me the problem is conservative mentality toward any change in the way to look into turbulence and to question the generality of N-S.

For example, for the numerical-tools, when I was in undergrad once I cam up with an idea, discuss it with couple of computer and CFD guys but seems there were no interest or perhaps the idea was too raw and not clear. I said, up to now CFD is based on discretizing the N-S into algebraic operations and write computer codes to perform these operations on the CPUs and Memory. Why not, move part of the duty of the code to the hardware levels. One simple example of mine was to come up with a type of 3D memory mixed with devices to perform algebraic operation on the memory itself … well, I was not aware of 2D memory addressing idea and … and I was told that yes regular memory are 1D accessible but the idea of 2D accessing exist in the memory industries. But are there any active research in the IC industries to advance this idea toward making ICs that they are performing CFD operations on the hardware level? This may looks very futuristic, but to the best of my knowledge since the first time I talked about it in my undergrad, I have not yet seen any one think about it at all. FPGA based on CFD operators are also a possibility: devices that can perform CFD operation but apparently they are limited to few layers thickness (to my knowledge) However, it is ok for now. We can connect hundreds of them in parallel and perform Laminar flow simulation in which communications between layers of fluid are less! All in all, what I mean is going toward making hardware-CFD-devices based on discretized equations. Roughly speaking, the speed of propagation of the information between the fluid-elements in the codes will be replaced by the speed of propagation of information in the IC….

For the models, some of my personal points of view are:
1) since to me turbulence occurs when the translation modes of molecules is not the dominant one; I would recommend performing LES but with models based on:
1-1) balance of translational and rotational-vibrational modes of molecule-energy or
1-2) even solving Lattice Boltzmann (LB) for the models to project the velocity field from the resolved field (from N-S solution) to the initial/boundary condition for a model-based on LB: the back and forth projection between LB based models and N-S resolved field …
1-3) models based on molecular-simulation: MD based model + N-S resolved field

DG (Discontinuous Galerkin) should be a very good candidate for the numerical scheme: solving N-S by DG to obtain the resolved field and then performing the LB models, MD models, or solving Schrödinger eqns inside the necessary elements …

It is a long time that I have been thinking of some new ideas in turbulence and vortex-identification-techniques. One of them is simply as follows:

Whatever we are calling turbulence occurs when the translational mode of energy of the fluid molecules is not the dominant mode of energy. (perhaps vibrational mode is the dominant one)

It seems to me that a recent paper (Complex Nonlinear Opto-Fluidity) of Segev and Christodoulides and their colleagues (Segev is a pioneer in Nonlinear-Opto-Fluidity and an authority in Nonlinear-Optics) at CLEO-QELS-2008 (http://www.cleoconference.org/) is along the same pathline.

They have found a coupling between transfer of angular-momentum from light (photon) to the fluid. I believe this is a preliminary sign in proving the aforementioned statement.

It would be interesting to extend their efforts with 2 main objectives:

1) Extension of their experimental efforts to lower-size particle and find correlation(s) between different molecules-modes-of-energy of & fluid-eddies.

2) Numerical Investigations: Studying Time-Dependent-Schrödinger-Equations & Navier-Stokes-Equations simultaneously in order to track the creation and evolution of vortical structures from quantum-turbulence.