Learned discretizations for passive scalar advection in a two-dimensional turbulent flow
Abstract
The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small-scale features of complex flows. Here we use a machine learning approach to learn a numerical discretization that retains high accuracy even when the solution is under-resolved with classical methods. We apply this approach to passive scalar advection in a two-dimensional turbulent flow. The method maintains the same accuracy as traditional high-order flux-limited advection solvers, while using 4 × lower grid resolution in each dimension. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The solver can achieve near-peak hardware utilization on CPUs and accelerators via convolutional filters.
- Publication:
-
Physical Review Fluids
- Pub Date:
- June 2021
- DOI:
- 10.1103/PhysRevFluids.6.064605
- arXiv:
- arXiv:2004.05477
- Bibcode:
- 2021PhRvF...6f4605Z
- Keywords:
-
- Physics - Computational Physics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Physics - Fluid Dynamics
- E-Print:
- 14 pages, 13 figures