Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations

TL;DR

This paper presents a machine learning-enhanced hybrid solver that corrects errors in coarse-grid turbulent flow simulations, enabling high-resolution results at reduced computational costs.

Contribution

It introduces a novel deep neural network approach to correct coarse-grid errors and recover high-resolution turbulent flow fields, improving simulation efficiency.

Findings

Successfully applied to 2D Rayleigh-Bénard convection at high Rayleigh number.

Significantly reduces computational expense of turbulent flow simulations.

Demonstrates accurate high-resolution flow predictions from low-resolution data.

Abstract

Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion. Turbulent flows are typically modeled by the Navier-Stokes equations. Direct Numerical Simulation (DNS) of the Navier-Stokes equations with sufficient numerical resolution to capture all the relevant scales of the turbulent motions can be prohibitively expensive. Simulation at lower-resolution on a coarse-grid introduces significant errors. We introduce a machine learning (ML) technique based on a deep neural network architecture that corrects the numerical errors induced by a coarse-grid simulation of turbulent flows at high-Reynolds numbers, while simultaneously recovering an estimate of the high-resolution fields. Our proposed simulation strategy is a hybrid ML-PDE solver that is capable of obtaining a meaningful high-resolution solution trajectory while solving the system PDE at a lower resolution. The approach has the potential to dramatically reduce the expense of turbulent flow simulations. As a proof-of-concept, we demonstrate our ML-PDE strategy on a two-dimensional turbulent (Rayleigh Number $Ra=10^9$) Rayleigh-B\'enard Convection (RBC) problem.