Reducing Spatial Discretization Error on Coarse CFD Simulations Using an OpenFOAM-Embedded Deep Learning Framework

TL;DR

This paper introduces a deep learning-enhanced CFD framework embedded in OpenFOAM to significantly reduce spatial discretization errors in coarse simulations, improving accuracy efficiently.

Contribution

It presents a novel open-source deep learning method integrated with OpenFOAM that improves coarse CFD simulation accuracy by learning from fine-grid data and replacing traditional differencing schemes.

Findings

Error reduced from 120% to 25% in training scenarios

50% error reduction outside training distribution

Efficient training with local physics features

Abstract

We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after projecting it to the coarse-grid discretization. We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values to produce velocities that approximate the down-sampled fine-grid data well. The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model. We automatically differentiate the CFD physics using a discrete adjoint code version. We present a fast communication method between TensorFlow (Python) and OpenFOAM (c++) that accelerates the training process. We applied the model to the flow past a square cylinder problem, reducing the error from 120% to 25% in the velocity for simulations inside the training distribution compared to the traditional solver using an x8 coarser mesh. For simulations outside the training distribution, the error reduction in the velocities was about 50%. The training is affordable in terms of time and data samples since the architecture exploits the local features of the physics.