Reducing spatial discretization error on coarse CFD simulations using an openFOAM-embedded deep learning framework

Engineering With Computers, vol. 41, pp. 1699–1720

Abstract

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.

Authors 5

1. Jesus Gonzalez-Sieiro corresponding

   University of the Basque Country · Basque Center for Applied Mathematics

   Affiliation as printed

   BCAM - Basque Center for Applied Mathematics, Bilbao, Spain

   University of Basque Country (UPV/EHU), Leioa, Spain

2. David Pardo

   Ikerbasque · University of the Basque Country · Basque Center for Applied Mathematics

   Affiliation as printed

   BCAM - Basque Center for Applied Mathematics, Bilbao, Spain

   Ikerbasque - Basque Foundation for Sciences, Bilbao, Spain

   University of Basque Country (UPV/EHU), Leioa, Spain

3. Vincenzo Nava

   Basque Center for Applied Mathematics · Tecnalia

   Affiliation as printed

   BCAM - Basque Center for Applied Mathematics, Bilbao, Spain

   TECNALIA - Basque Research and Technology Alliance (BRTA), Derio, Spain

4. Victor M. Calo

   Curtin University

   Affiliation as printed

   School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, Australia

5. Markus Towara Aachen Software and Tools for Computational Engineering

   RWTH Aachen University

   Affiliation as printed

   Software and Tools for Computational Engineering, RWTH Aachen University, Aachen, Germany