Hi all! I defended my Ph.D. thesis back in 2019 and I also served as the creator and moderator for the subreddit r/FluidMechanics for a long time. I think with that I have gathered enough experience and courage to answer some of your queries. Some broad topics that I can answer questions on are:
- computation fluid mechanics
- scientific programming and HPC
- nonlinear shallow water equations
- statistical description of turbulence: spectra, energy budget etc.
- experimental methods: PIV
- stratified turbulence
- academia
- navigating your career pre- and post-Ph.D.
Ask away!
In games what I think they do is a technique called smooth partical hydrodynamics, which simply put does not solve the Navier Stokes equations (the preferred classical model for fluids), but moves solid spheres around which collide and interact.
The right way would be to solve the full 3D NS equations, but like you said it is very expensive to do. But doing a 2D simulation on a laptop is very much possible. This hands on series is a good start
https://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/
There are also other models like a lattice boltzmann equations which this web app solves
https://physics.weber.edu/schroeder/fluids/
For more detailed study a theoretical book would be Fluid Mechanics by Kundu and Cohen and a computational book would be CFD 3 volume series by Hoffmann and Chiang.
Thanks! The Jupyer notebooks seem like a good starting point. I had used Burger’s equation but it was from the point of view of using it as a nonlinear dynamical system for state estimation, rather than from a fluid mechanics understanding of it. Are the textbooks you mentioned the recommended standards for this field?
Kundu and Cohen is defintely universally acclaimed to hit the right balance between being concise, readable while allowing the reader to gain a deep understanding of the fundamentals.
Hoffman is a good book for understanding some numerical methods, but there may be other books.