Towards Fast Aerodynamic Simulations with Machine Learning Corrections for Discretization Errors

Computational fluid dynamics has become an important method for aerodynamic analysis, supplementing or partially even substituting wind tunnel experiments or flight tests. A spatial discretization on so-called grids is used to approximate a solution of the boundary-value problem of interest. In general, increasing the number of degrees of freedom, the accuracy of the approximate solution improves, typically going hand-in-hand with additional computational complexity. Consequently, conducting a rigorous amount of accurate simulations, as for example for a complete flight envelope, is possibly infeasible. Thus, there is a need for novel approaches to reduce the overall numerical cost to allow for faster and inexpensive design process iterations. This work shows how machine learning methods can be employed as a post-processing tool to improve the accuracy of comparably inexpensive low-fidelity results, including coarse grid finite volume and low-order discontinuous Galerkin simulations. It is shown that using two different regression models, a random forest and a graph neural network, inaccurate simulations can be corrected to approximate the high-fidelity simulation projected to the low-fidelity discretization. Improved flow fields are obtained as well as improvements in pressure and lift coefficient. A main limitation of the method involves the loss of accuracy due to projection, resulting in less significant corrections of velocity gradient dependent values, such as friction and drag coefficient. Independent of the chosen discretization, be it finite volume or discontinuous Galerkin, results show possibilities and drawbacks of applying data-driven methods to correct low-fidelity simulations. It is anticipated that the proposed method can be used to quickly iterate over simulations conducted within a chosen design space, which could entail a given flight envelope. Furthermore, this work is a promising baseline for further research, including the correction of unsteady simulations and the use of a machine learning based error indicator for refinement strategies.