Data-Driven Aerodynamic Kernel Functions for Boundary Element Flow Models

A method for predicting aerodynamic flows using learned kernel functions for the underlying boundary element problem is introduced. A formulation for the baseline potential flow kernels is presented, followed by the methodology of learning the kernel from a computational fluid dynamics dataset. These kernels are given an arbitrary formulation, and a gradient-based approach is used for the learning step, restricting the description to differentiable functions. The problem of relearning a potential flow vortex is presented, followed by learning steady 2D compressible flow around thick airfoils by using a neural network kernel. The resulting learned kernel solution yielded more accurate velocity and pressure distributions than the potential flow baseline. Lastly, the impact of enforcing rotational and translational invariance properties on the kernel definitions is investigated, which finds that more generalizable models can be created at the expense of accuracy.