Influence of Mesh Sensitivities on Computational-Fluid-Dynamics-Based Derivative Calculation

To clarify the influence of mesh sensitivities on the computational-fluid-dynamics-based derivatives, a theoretical deduction and treatment of the mesh sensitivities are carried out, yielding an explicit mathematical formulation for issues of concern. Numerical tests focusing on aerodynamic shape derivatives, within the context of a transonic viscous flow passing through an RAE2822 airfoil, are conducted to validate the theoretical analysis. The automatic differentiation (the adjoint and tangent modes), as well as the finite difference, are applied to resolve the gradient information. Various mesh-deformation strategies, including the finite element analog, the spring analog, the original radial basis function interpolation, and a new modified radial basis function method, are applied to provide different mesh-sensitivity solutions. The numerical results confirm that mesh sensitivities are essential for the geometry-related numerical derivatives, and the reliance is independent of the perturbation magnitude and the gradient prediction algorithms. Furthermore, several basic necessary conditions for a reliable mesh-sensitivity solution conducted by mesh-deformation strategies are derived from numerical experiments. Among the different mesh-deformation strategies, the new modified radial basis functions and the finite element analog outperform the other ones in derivative calculation of the given RAE2822 case.