A differentiable software suite for accelerated simulation of turbulent flows

TL;DR

This paper introduces IncompressibleNavierStokes.jl, a Julia package for efficient, differentiable simulation of turbulent flows, enabling neural network training within large-eddy simulations at high resolutions.

Contribution

It presents a novel differentiable, hardware-agnostic solver with optimized memory usage, supporting neural network closure models in turbulence simulations.

Findings

Validated turbulent channel flow results against reference data.

Achieved high-resolution simulations up to 840^3 on a single GPU.

Demonstrated efficient reverse-mode automatic differentiation for neural network training.

Abstract

We present IncompressibleNavierStokes.jl, an open-source Julia package for solving the incompressible Navier--Stokes equations on staggered Cartesian grids. The package features matrix-free, hardware-agnostic kernels that are compiled from a single source for multi-threaded CPU or GPU execution, and hand-written adjoint kernels for all discrete operators, enabling efficient reverse-mode automatic differentiation through the entire solver. This differentiability allows neural network closure models to be trained a-posteriori while embedded in a large-eddy simulation. Memory optimizations permit double-precision direct numerical simulations at resolutions up to $840^3$ on a single GPU. The software design, numerical methods, hardware performance, and integration of neural network closure models are described, and results for turbulent channel flow are validated against reference data.