Investigation of discontinuous Galerkin methods in adjoint gradient-based aerodynamic shape optimization

Abstract

This work develops a robust and efficient framework of the adjoint gradient-based aerodynamic shape optimization (ASO) using high-order discontinuous Galerkin methods (DGMs) as the CFD solver. The adjoint-enabled gradients based on different CFD solvers or solution representations are derived in detail, and the potential advantage of DG representations is discovered that the adjoint gradient computed by the DGMs contains a modification term which implies information of higher-order moments of the solution as compared with finite volume methods (FVMs). A number of numerical cases are tested for investigating the impact of different CFD solvers (including DGMs and FVMs) on the evaluation of the adjoint-enabled gradients. The numerical results demonstrate that the DGMs can provide more precise adjoint gradients even on a coarse mesh as compared with the FVMs under coequal computational costs, and extend the capability to explore the design space, further leading to acquiring the aerodynamic shapes with more superior aerodynamic performance.

Figures (25)

• Figure 1: The workflow for the adjoint-enabled gradient-based ASO.
• Figure 2: Computational grids with different levels of the NACA-0012 airfoil test case.
• Figure 3: Solutions (density) obtained by different solvers on various grids of the NACA-0012 airfoil test case.
• Figure 4: NACA-0012 $C_p$ distributions between CFD data and experimental data.
• Figure 5: $C_d$ convergence of the NACA-0012 airfoil test case.