An application of space-filling curves to improve results of turbulent aerodynamics modeling with convolutional neural networks

Abstract

When carrying out calculations for turbulent flow simulation, one inevitably has to face the choice between accuracy and speed of calculations. In order to simultaneously obtain both a computationally efficient and more accurate model, a surrogate model can be built on the basis of some fast special model and knowledge of previous calculations obtained by more accurate base models from various test bases or some results of serial calculations. The objective of this work is to construct a surrogate model which allows to improve the accuracy of turbulent calculations obtained by a special model on unstructured meshes. For this purpose, we use 1D Convolutional Neural Network (CNN) of the encoder-decoder architecture and reduce the problem to a single dimension by applying space-filling curves. Such an approach would have the benefit of being applicable to solutions obtained on unstructured meshes. In this work, a non-local approach is applied where entire flow fields obtained by the special and base models are used as input and ground truth output respectively. Spalart-Allmaras (SA) model and Near-wall Domain Decomposition (NDD) method for SA are taken as the base and special models respectively. The efficiency and accuracy of the obtained surrogate model are demonstrated in a case of supersonic flow over a compression corner with different values for angle α and Reynolds number Re. We conducted an investigation into interpolation and extrapolation by Re and also into interpolation by α.