To be honest, I don't think it is possible to address an economical value for your CFD code. You have to know that there are open-source CFD codes that can be downloaded for free, they are commonly used in the world and users can communicate their idea in the forum. What is more, at present a code needs to be programmed for parallel computing.

Last, FEM is now developed in terms of the DG formulation.

Thanks for your reply.

Concerning the say that there are free open source CFD codes available online such as OPENFOAM, it’s developers report that the code has about one-million lines of coding!!!. Honestly, can anyone tell me that he/she has read and fully understood these one-million lines of coding?? This might be possible but to maybe just few very intellectual persons around the world. My code is around 5000 lines. Just because something is available in the market or the internet it means that we don’t need to see something different of the same kind. Diversity must always be there and every product no matter you might think of its importance and value has a value of its own. Would Rolls-Royce be the only car that we should have?? Should Boeing or Airbus be the only aeroplanes that should exist?? Should we drink only Pepsi??

As mathematical and numerical models and codes are all about predictions, one cannot be sure of their results no matter how many validation tests by any model or code are made. This is because models and codes are tested and validated under certain set of conditions of model parameters and boundary conditions which are often different than the conditions under which the intended problem simulation or prediction is required. This is true no matter you have the best available software in the market (e.g. OPENFOAM , ANSYS, FLOW3D, COMSOL Multiphysics, ABAQUAS, …etc.) as any single software or model still represents one point of view as far as mathematical treatment of the problem at hand.

Therefore, using only one model to investigate a certain phenomenon might not be the best approach as there is no assurance that a single model will produce reliable results. One option to overcome this issue at least partially and not completely is to use a different model or even using several models to tackle the problem at hand. This will allow comparison of the simulation results and if the models’ results are within a narrow and accepted range then the results would have more confidence than when using only one model.

Another reason is that commercial software(s) usually are very general in order to cover as many cases as possible but often the problem at hand would have unique and new features that might not be built yet in the commercial software model and asking the company providing the software for modelling these new features will cost more money and waiting time. There is no guarantee these models’ output would be reliable as these models have very complex structure and any modification even if it is slight requires a lot of work to do. In the meantime, in-house built models usually do not have a complex structure and are relatively easy for almost all modifications.

Take for example the well-known ANSYS CFD code. There are huge number of publications using ANSYS in almost all CFD applications that you might think of (flows in combustion engines, turbines, ducts, pipes, point-source pollution…etc.), so you get the impression that it models every thing you can think of; with near exact precision. One can notice that in all the publications about ANSYS they list the equations of motion and the equations for the turbulence model as a closure such as K-e or K-W or else; without explicitly writing the exact expressions for the turbulent stresses. One can assume that it seems that it is a linear turbulent stress-strain rates are used. However, the linear turbulence models are by definition incapable of simulating eddies and secondary motion due to corners or free surfaces or surface roughness irregularities. I am not sure if the current version of ANSYS can predicts the 8 eddies structure for flow in a square duct where secondary motion are due to corner effects. So, to model any flow that include these features (I think almost every flow contains corners, free surface or irregular roughness) a nonlinear turbulent stress-strain rate must be used. Of course due to the nonlinear character it might be extremely difficult to always obtain convergence which is one reason to not including them in commercial software in addition to the mathematical difficulty and complexity of their numerical modelling. The same argument could be presented for free-surface flows and existence of the free surface in turbulent flows generates surface eddy structure. This leaves the floor to in-house built models as they can be case specific with less generality that gives more freedom and flexibility. I think that ANSYS and similar software(s) are not that magical in spite the magical three-dimensional images the vendors or users are presenting.

Another good reason is that commercial software is supplied as application software, i.e., the source code is not provided. This means that it is like a black box where the inside modelling details are hidden. On the other hand, in-house models can provide the source code which make them very transparent and the inside modelling details would be visible.

While I could agree with you about of your observations, there is much more to be considered if you hope to get a value from the CFD market.

I suggest you to open a post on the cfd-online forum attaching your pdf

https://www.cfd-online.com/Forums/main/

so that you can discuss with other people currently developing CFD codes.

I agree with Filippo, CFD-online would attract more answers from developers.

Let me also clarify that both OpenFOAM and Code_Saturne (not sure about SU2) have today the most advanced turbulence models, which include non linear ones as well. This is especially so for Code_Saturne, that has been the preferred choice for developments in Manchester. If we allow to consider closed source codes, well, Ansys Fluent just has the same capabilities with several algebraic non linear and full Reynolds Stress Models. Also, let's not forget that Florian Menter is in charge for that in Ansys.

I'm not really into free surface flows, so I can't really tell, but the same reasoning applies here. There are several options for the most diverse conditions. In general, coming from commercial development, let me tell you that every low hanging fruit that works for general solvers with unstructured grids is generally a no-brainer and eventually gets in (as long as the model is actually helpful).

This just to clarify that if you intend the CFD solver market as a battle field, it's not the early 90's Fluent that you're going to face. It's 2022, and there is also Siemens with Star, Cadence with ex-Numeca, Altair with several products, and few other less known vendors of high quality.

This, however, it's not the main point here, in my opinion, in valuing your code. I haven't read your thesis, but it seems that the main point of your development is sitting there open to everyone. So, if it is usable for general flow solvers, I guess you are left with little to none, because everyone can already use your model without your code. Also, 5k lines of code is very little in this case. If you want a comparison, I have seen fully original source codes of that length sold, non exclusively, for about 30k USD. So, if ever, in your case the amount should be much lower. Also, note that we are speaking about selling the source code for third party reuse at their wish, not licensing the code here.

So, excluding, de facto, the previous hypothesis as meaningful, let's assume that your unique modeling is not usable in other codes or that not everything is open to everyone, which is basically the same. I am myself into CFD code development and a fully parallel unstructured solver with basic functionality (multi-zone with CHT, URANS, steady/unsteady, implicit/explicit, incompressible/compressible, scalars and all the machinery to make it usable like a major commercial solver) can be fit in 20k-25k lines of code. So, at 5k, I assume your code is weak on some of these basic features. So, we are presumably speaking of a niche code that can eventually do some specific things very well, but doesn't seem more generally usable.

Thus, finally getting to your question, I think the valuation for your code is totally up to the niche you are addressing, the problem you are solving and how costly it is for your niche. If your code solves a multi-billion dollar problem for a very rich industry and nobody else can solve that same problem, people would pay as much as you ask, even if your code was still written on punch cards or could run on ancient hardware of limited availability. The CFD market is full of verticals that get exploited, but it is really up to you to actually know if your code fits any of them.

But if you don't address a specific unsolved problem nor have a more general usability, I don't think you can really monetize your code.

Also, I didn't mention this but, the code must obviously be also usable by a general audience. If it requires expert adjusting for every case, it becomes extremely difficult to use and very few will be able to, even if it addresses a multi-billion dollar problem.

Thanks a lot for your valuable comments and I did join CFD-online as recommended by Dr. Filippo . Please find in the attached file a brief description that gives you an idea about the basic or foundation of my CFD code. The code is originally for steady, fully developed flow in the cross sectional plane (Y-Z plane) normal to the main flow X-direction (two dimensional geometry), but with three-dimensional velocities in the cross sectional plane (U, V, and W), and K-epsilon turbulence model for evaluating the turbulent viscosity appearing in the nonlinear algebraic stress-strain rate relations, Speziale (1987). The code was later substantially developed and extended to include unsteady and fully-three dimensional conditions. Also, two versions are later developed to include large scale two-dimensional flows in the X-Z and X-Y planes.

Sure it is not the 90’s where my code was facing Fluent, however, I see that most current codes are focusing mainly on the three dimensional meshing capabilities and the 3D geometrical representations with little attention paid to the basic fluid dynamics.

It should be noted that the original code has not been published in any form anywhere. It should be mentioned that the 5K lines are for the Fluid dynamics part only but there are parts with 1500 lines for the mesh generator, 500 lines for preparing matrix storage (Sky line or Banded matrix), and 2500 lines for scalar transport (heat or mass), so adding all these parts together makes about 8500 lines in total. However, it is not by the size as far as code comparisons if the same functionality exists. I see the small number of lines as an advantage as fewer lines are more efficient in understanding all the programming details and making things easier for further developments as long as the same functionality exists in comparison with other codes.

I am open to the two options that you mentioned, namely: selling the source code for third party reuse at their wish, or selling the code with full-licensing. I think the uniqueness of my code over other codes includes using the non-linear algebraic stress model developed by Speziale (1987) in ducts and closed channels, while that of Naot and Rodi (1982) is used in open channels with new algebraic surface proximity functions. My code has a lot of flexibility in representing the boundary conditions such as periodic roughness on the walls or inside the flow domain representing non-homogenous properties or non-isotropic conditions owing to the flexibility offered by the finite element method. Please see Table 1 in the attached file for other comparisons with ANSYS and OPENFOAM.

As my code deals with the flow velocities, heat and mass, it definitely could be considered a general purpose CFD code. It is very much user-friendly. The code could be adopted by whoever is interested to convert it to an application software with commercial features. This means that it is a good opportunity for a new CFD company that is willing to introduce a different type of CFD code.