A data-driven vorticity-confinement approach for compressible aerodynamics prediction on very-coarse meshes

How to predict aerodynamics accurately and quickly is the focus of attention in this era, especially in the initial design stage of aircraft. In this study, we address the treatment of the shear layers in low-resolution mesh for compressible flow. The method is proposed to compensate for the inevitable increase in the thickness of the boundary layer and the reduction of the velocity gradient due to the coarse mesh by introducing a vorticity confinement term as the body source in the momentum equation. The confinement parameter determines the strength of the vorticity confinement term for the reduction of numerical dissipation. In order to extend this method to various flow conditions, a surrogate model is established using ordinary least squares (OLS) to link the confinement parameter to local flow features that reflect turbulence characteristics. Ultimately, the DVC approach is successfully applied to transonic boundary layer and free shear flow. The accurate prediction is achieved for the pressure coefficients on a transonic airfoil by capturing the λ structure of the buffet offset. The mean relative error of the pressure coefficients on the airfoil is reduced from 48.1 % (by inviscid Euler approach) and 26.7 % (by RANS) to 1.8 % (by DVC approach). Given that the current method is assimilated through a flat boundary layer, better results can be obtained by introducing flows that are related to the actual conditions for data assimilation. It thus serves as a novel data-driven approach for rapid prediction of specific flow structures and aerodynamic performances in aerospace engineering.