  Physics-informed neural networks (PINNs) have recently become a new popular
method for solving forward and inverse problems governed by partial
differential equations (PDEs). However, in the flow around airfoils, the fluid
is greatly accelerated near the leading edge, resulting in a local sharper
transition, which is difficult to capture by PINNs. Therefore, PINNs are still
rarely used to solve the flow around airfoils. In this study, we combine
physical-informed neural networks with mesh transformation, using neural
network to learn the flow in the uniform computational space instead of
physical space. Mesh transformation avoids the network from capturing the local
sharper transition and learning flow with internal boundary (wall boundary). We
successfully solve inviscid flow and provide an open-source subsonic flow
solver for arbitrary airfoils. Our results show that the solver exhibits
higher-order attributes, achieving nearly an order of magnitude error reduction
over second-order finite volume methods (FVM) on very sparse meshes. Limited by
the learning ability and optimization difficulties of neural network, the
accuracy of this solver will not improve significantly with mesh refinement.
Nevertheless, it achieves comparable accuracy and efficiency to second-order
FVM on fine meshes. Finally, we highlight the significant advantage of the
solver in solving parametric problems, as it can efficiently obtain solutions
in the continuous parameter space about the angle of attack.
