Controlling extreme energy events in turbulent flow (2D Kolmogorov flow).
If you plan to use this code for research purposes that may result in publications, please contact me first at [email protected].
This project assumes you have the following Python libraries installed:
- Jax (https://jax.readthedocs.io/en/latest/installation.html)
- Matplotlib and seaborn for visualization
The PseudoSpectralNavierStokes2D class expects a FlowConfig class argument. For simplicity, the FlowConfig contains default values. The user can, however, specify flow parameters such as:
- Reynolds number (flow.Re)
- Grid size (flow.grid_size)
- Forcing wavenumber (flow.k)
- Timestep
The vorticity field can be initialized with flow.initialize_state() for simplicity, as it creates a divergence-free field by default.
This project uses a fourth order implicit-explicit Runge-Kutta time stepping scheme from [2]. The user can specify the length of the simulation and the uniform interval desired for saving:
dt = 0.001
end_time = 100
save_interval = 1
total_steps = int(end_time // dt)
step_to_save = int(save_interval // dt)
vorticity_hat0 = flow.initialize_state()
step_fn = transient.RK4_CN(equation, dt)
end_state, full_trajectory = transient.iterative_func(step_fn, vorticity_hat0, total_steps, step_to_save)
In this case, the simulation trajectory will be stored in full_trajectory.
For computing and visualizing the extreme energy events in Kolmogorov flow, refer to kolmogorov_demo.ipynb.
The references used when creating this code:
[1] Z. Yin, H.J.H. Clercx, D.C. Montgomery, An easily implemented task-based parallel scheme for the Fourier pseudospectral solver applied to 2D Navier–Stokes turbulence, Computers & Fluids,Volume 33, Issue 4, 2004, Pages 509-520, ISSN 0045-7930, https://doi.org/10.1016/j.compfluid.2003.06.003.
[2] G. Dresdner, D. Kochkov, P. Norgaard, L. Zepeda-N´u˜nez, J. A. Smith, M. P. Brenner, and S. Hoyer, “Learning to correct spectral methods for simulating turbulent flows,” 2022.