Correcting the discretization error of coarse grid CFD simulations with machine learning

Abstract

Computational fluid dynamics is a cornerstone for the modern aerospace industry, providing important insights on aerodynamic analysis while reducing the need of expensive experiments and tests. Nevertheless, simulations of complex geometries are often performed on a discrete spatial domain too coarse to capture all relevant physical phenomena for the sake of lowering the computational cost. A consistent spatial discretization on so-called grids approximates the analytical solution of the partial differential equation with increasing number of discrete points. Such a grid refinement study is an expensive method to assess the general grid quality. This work shows that machine learning as a post-processing tool is capable of improving coarse grid simulations, even if not converged. The results show that three machine learning models varying in their complexity, namely the random forest, the neural network, and the graph neural network, are capable of finding patterns in coarse grid simulations. These patterns are used to predict the discretization error to approximate the field variables of interest of the corresponding fine grid simulation mapped onto the coarse grid. Initial training and testing is performed on the RAE2822 airfoil leading to corrected flow fields, improved surface integrals and coefficients, even when shocks are present. Additional tests are performed on the RAE5212 airfoil, showing the generalization limits of the trained models. The proposed method promises to reduce computational expenses while increasing the accuracy of the coarse grid results which works locally, e.g. it corrects the error for each cell individually and is therefore not restricted by the number of grid points. The presented results obtained by the machine learning models during post-processing are a promising baseline for more integrated developments, where the models will interact in a dynamic fashion with the flow solver to further improve coarse grid simulations.