More patents, less papers

Recently, my second journal article in the series (The Unsteady Full Multi-wake Vortex Lattice Method: a full rolled-up detached vorticity approach [1]) was declined for publication four months after its acceptance (already peer-reviewed) in a second quartile (Q2) journal. This is not due to lack of consistency in methodology or results, but due to lack of the payment of the Article Processing Charge (APC)!, which neither the university nor the Science Council 'can' afford, although both of them are included in the remaining two articles, published without APC in a Q1 journal. Fortunately, I have never been interested in becoming an paper-publishing researcher to try to play the game imposed by the current academic system; I have only published my research as a requirement to obtain my PhD degree. However, this does not mean that I believe that knowledge should be restricted; ideally, the knowledge should be open and universal, especially when it concerns the foundations of a particular field, as in this case.

Fig. 1 Patent's cover (online version).

Nevertheless, I firmly believe that intellectual and industrial property is a right that every technologist, scientist, inventor, or artist should have; no one should make a profit at the expense of someone else's inventiveness*. For this reason, I decided to protect the computational development made during my doctoral studies with a patent, first with a provisional one at the United States Patent and Trademark Office (USPTO) and finally looking for extending its protection to an international one at the World Intellectual Property Organization (WIPO) through the Mexican office (IMPI); since the beginning of this process, the university patent office refused to fill the application for lack of an associated researcher there...At this point, such an international application has been declared patentable in the first instance (meets novelty, inventive step and industrial applicability) by the International Searching Authority (ISA) at the USPTO. The published version (originally in Spanish) of such an application (then: PCT/MX2024/050007; now: WO/2024/136634) can be found here: WO2024136634 MÉTODO Y SISTEMA DE VORTICIDAD DESPRENDIDA DE SUPERFICIE COMPLETA PARA RESOLVER LA DINÁMICA DE FLUIDOS (wipo.int). The English version (which may still contain translation errors) can be downloaded from: FULL-SURFACE DETACHED VORTICITY METHOD AND SYSTEM FOR SOLVING FLUID DYNAMICS

As you can see, the methodology and results are exactly the same as presented in the three related articles, but in a patent format, described in extreme detail in such an invention. But what the hell! will this patent be the panacea of fluid dynamics? Well, too many people, including scientists and researchers, are incapable of understanding that simple problems must be solved before trying to solve more complex ones. That is why today we see an increasing number of new complex schemes, models and bombastic methods and techniques to approximate mesh-based Computational Fluid Dynamics (CFD) solutions, which require more and more computational resources to solve even relatively simple cases (even in the two-dimensional case yet!). Fluid dynamics is not as complex as some people make it out to be! It is quite similar to solving solid mechanics since fluid elements can be represented by deformable-rigid bodies (e.g., vortex tubes). This is nothing new, such a concept is what vortex methods are based on. So why do we still want to solve DY-NA-MICS (which inherently implies motion!) by FIXED points in space? I think that such a question should have been asked seriously several decades ago. 

Fig. 2 Two vortex rings during collision. Vorticity is the fundamental variable that governs fluid motion. https://legendary-digital-network-assets.s3.amazonaws.com/wp-content/uploads/2018/07/14041934/vortex-rings.jpg

Is this method the Holy grail of fluid dynamics? This patent helps to explain and justify a fundamental process in fluid dynamics: flow separation and its precise temporal evolution. Therefore, all future more complex developments in this field of research should be based on this approach because it simplifies the understanding of fluid motion to the limit. For this reason, no more than one independent claim (the most important part of a patent) is needed; less is more. But, what is the difference between this application and other granted patents for vorticity-based CFD methods?

A similar vortex method is described in patent JP2004126925A. However, the main difference between the two methods is the mechanism (viscous vs. inviscid) of vorticity generation near a solid surface. In such an invention, a vortex blob is generated per discretized surface element based on additional and more complex computations, since the generation of vorticity is based on viscous calculations (i.e., shear stresses between layers). It is important to note that a vorticity generation based on a viscous assumption would contaminate the numerical solution, since according to a vorticity generation theory, such a mechanism is purely an inviscid process [2], and viscosity is only implied after the instantaneous vorticity generation.

Fig. 3 Viscous scheme for generation of vorticity at solid surface (Ojima and Kamemoto, 2000). Too complex and inaccurate!

Another related patent is US20210124861A1 which focuses on algorithms for removing vortex loops and reconnecting filaments to save computational time, in the context of the vortex filament method (VFM). For the generation of surface vorticity, it refers to a vortex tube generator module based on the generation of vorticity through a set of vortex sheet layers (described in detail in a related patent US6512999), which represents a viscous approach (similar to the shown in Fig. 3). As for the turbulence treatment, since the present invention focuses on solving fundamentals and numerical accuracy rather than on implementation or computational efficiency (e.g., Fast Multipole Method; FMM), no turbulence model is implemented. Theoretically, in the upper limit of the vortex element method (VEM) discretization, all turbulent scales are explicitly solved, similar to a mesh-based direct numerical simulation (DNS) that does not require either wall or Kolmogorov’s scale modeling. Now, turbulence, that constitutes one of the most challenging problems in fluid dynamics, can be analyzed from its fundamental constitution: vorticity, with precise squeezing-stretching.

Fig. 4 Leonardo da Vinci's description of turbulence.

Now it is time to enter the appeals phase of the patent, which will probably be the hardest part (or probably not). So maybe it is not right to try to answer the question left open before until this phase is over. In the meantime, I will be looking for ways to continue developing my own ideas, despite the challenges ahead:

*ingenuity (I do not feel comfortable using this word because in my mother tonge it sounds the exact opposite!).

"Simplicity is the ultimate sophistication." Leonardo di ser Piero da Vinci.

[1] (PDF) The Unsteady Full Multi-wake Vortex Lattice Method: a full rolled-up detached vorticity approach (researchgate.net)

[2] A fundamental question of fluid dynamics