Fluid Flow, Heat Transfer, and Python

full EDIT:

I will tell a little more about the whole problem. The project is at an early stage, and my question actually concerns only a narrow part of the thing.

ultimate goal:
I am currently trying to simulate a stream of hot air around a hard obstacle in Python. I have a constant flow of air, the flow in the volume is temporary and turbulent. The goal of the whole exercise is to understand how - the air flow behaves - the obstacle heats up the
air cools and the air pressure drops

done so far:
Not much, it's an early stage. I have a 2d rectangular area and a round obstacle. The grid becomes finer at the boundary between the mass and the obstacle, since it is here that interesting material occurs. Currently, I am considering only airflow, the absence of convection or heat transfer. I am using the FEniCS software collectionto solve the Navier-Stokes equation. Fenics comes with an example for solving NS using the Chorin projection method, I adapted this example to my settings. I model a solid as a region without a boundary sliding condition (i.e., I set the air flow rate to zero). The solver still solves the NS equation in this area, in particular, the pressure inside the obstacle varies with time. This is probably the best idea to avoid this and limit the NS solver in bulk. But at the moment, I do not think that this greatly affects the speed.

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