A nonlinear sensitivity solver for optimization and rapid design aerodynamic shape space exploration

A new nonlinear sensitivity solver has been derived and implemented within the US3D Computational Fluid Dynamics code. The nonlinear sensitivity equation is derived from the discrete finite-volume formulation of the Navier-Stokes equations. The sensitivity solver uses a steady-state solution of the flow variables as an initial starting point. A change to the system is then introduced in the form of a grid or flow parameter perturbation. The perturbed system is solved using an implicit method and rapidly converged until the fluxes are properly balanced. The new solution at the perturbed state is a completely valid solution of the same Navier-Stokes equations used by the CFD solver. Because of this, the sensitivity solver can accurately predict highly nonlinear events such as shock wave movement and shock boundary layer interactions. In this work, the nonlinear sensitivity solver is used to efficiently calculate objective function gradients within an inlet optimization cycle. Additionally, the sensitivity solver is used as a convergence acceleration mechanism to rapidly simulate an angle of attack sweep of a three-dimensional inward-turning scramjet inlet.