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:
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
How to implement the changes to the final part of Lorena Barba's tutorial should be fairly obvious by the time you get there.