Solving Turbulent Rayleigh-Bénard Convection using Fourier Neural Operators

Abstract

TODO

Rayleigh-Bénard Convection

This work uses Fourier Neural Operators to model Rayleigh-Bénard Convection (RBC). RBC describes convection processes in a layer of fluid cooled from the top and heated from the bottom via the partial differential equations:

Rayleigh-Bénard Convection

$$\begin{aligned} & \frac{\partial u}{\partial t} + (u \cdot \nabla) u = -\nabla p + \sqrt{\frac{Pr}{Ra}} \nabla^2 u + T j \\ & \frac{\partial T}{\partial t} + u \cdot \nabla T = \frac{1}{\sqrt{Ra Pr}} \nabla^2 T\ \\ & \nabla \cdot u = 0 \\ \end{aligned}$$

The surrogate models are trained on data generated by a Direct Numerical Simulation based on Shenfun with the following parameters:

Parameter	Value		Parameter	Value
Domain	((-1, 1),(0, $2\pi$))		($T_t$, $T_b$)	(1,2)
Grid	64 x 96		$\Delta t$	0.025
Rayleigh Number	{1e5, 1e6, 2e6, 5e6}		Episode Length	300
Prandtl Number	0.7		Cook Time	200

Citation

If you find our work useful, please cite us via:

@article{todo,
  title={Solving Turbulent Rayleigh-Bénard Convection using Fourier Neural Operators},
  author={Straat, Michiel and Markmann, Thorben and Hammer, Barbara},
  journal={},
  year={}
}

Setup

pip install ...

How to run

python ...