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CFDPython reviews and mentions
 Which one is best for numerical simulations for fluid mechanics [mostly linear terms].

Poisson's Equation is the most powerful tool not yet in your toolbox
There are many different ways to do what you'd like. The easiest starting point would probably be this tutorial: https://github.com/barbagroup/CFDPython
But that won't handle turbulence. The real "turbulence problem" is that computing actual turbulent flows requires enormous computational resources. So instead of solving the NavierStokes equations, related equations with lower computational cost are solved. Because of how these equations are developed, they require modeling of "unclosed" terms, and this is a likely source of inaccuracy.
If you want something relatively simple, you could take the RANS approach and use the SpalartAllmaras model:
https://www.cfdonline.com/Wiki/Introduction_to_turbulence/R...

Complexity Explained
I sniff an air of condescension; what’s your goals therein? Are you posturing your ‘maths’ knowledge?
I thought I was explicit in my criticism of “notation only” explanations, but perhaps a positive example would be more explicit.
https://github.com/barbagroup/CFDPython
This repo explains computational fluid dynamics (an example of a complex system!) from “what is a python function” to “2d Navier stokes”.
It shows the work of how to discretize ‘latex beautified’ notation, shows the relationship between the computations and the notation, and even explains when their LaTex strays from “conventional use of notation” and why.
The authors even throw in traditional handwritten board lecture videos if that helps you learn better.
complexityexplained reads like it’s written by the SpiderMan points at SpiderMan meme.

AeroPython: Classical Aerodynamics with Python
See also by the same professor CFD Python: 12 Steps to NavierStokes: https://github.com/barbagroup/CFDPython

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barbagroup/CFDPython is an open source project licensed under GNU General Public License v3.0 or later which is an OSI approved license.
The primary programming language of CFDPython is Jupyter Notebook.