Investigation of Using High-Order Discontinuous Galerkin Methods in Adjoint Gradient-Based 3D Aerodynamic Shape Optimization

Based on recent work by He et al. (Computer Physics Communications 286 (2023): 108660), this work develops a robust and efficient workflow for 3D aerodynamic shape optimization (ASO) based on the discontinuous Galerkin method (DGM) with solution remapping technique. It is theoretically found and numerically validated through 2D cases that the DGMs can provide more precise adjoint-enabled gradients even on a coarse mesh as compared with the FVMs under coequal computational costs. A number of 2D and 3D intricate cases are tested to illustrate the potential advantages of the DGM-based ASO workflow in terms of computational efficiency and final optimization results. The results demonstrate that the solution remapping technique can save around $50\%$ of the computational time. Moreover, the DGM-based workflow extends the capability to explore the design space, leading to aerodynamic shapes with superior performance.