Comparison of Finite Volume and High Order Discontinuous Galerkin Based Aerodynamic Shape Optimization

Aerodynamic shape optimization (ASO) requires a robust, accurate, and efficient flow solver. The second-order finite volume method (FVM) has been shown to satisfy these constraints when using a sufficiently fine mesh. However, during aerodynamic shape optimization, there are large geometry and flow solution changes that can lead to a decrease in solution accuracy over the course of the optimization. If the solution loses accuracy, the optimizer can find a spurious optimum. The discontinuous Galerkin (DG) method yields high-order accurate solutions that have less discretization error. However, the higher accuracy comes at a higher computational cost, so the advantage of DG is not always clear. DG is suitable for both local order and mesh refinement which can allow it to be more accurate per degree of freedom than the FVM. In this work we show the benefits of using DG over FVM for optimization. We also develop a strategy for p-adaptation during optimization that reduces computational cost and obtains the same optimum as a fine-space solution.