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CFDPython
A sequence of Jupyter notebooks featuring the "12 Steps to Navier-Stokes" http://lorenabarba.com/
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InfluxDB
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Here is my implementation in python of the Poisson equation on an arbitrary 2D domain using the finite element method. I used this for teaching a course in partial differential equations:
https://github.com/daleroberts/poisson
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 Navier-Stokes 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 Spalart-Allmaras model:
https://www.cfd-online.com/Wiki/Introduction_to_turbulence/R...
https://www.cfd-online.com/Wiki/Spalart-Allmaras_model
The article explain clearly. Made a toy canvas to play with poisson https://github.com/beenotung/poisson-canvas