Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

Abstract This paper presents a gradient-based aerodynamic shape optimization framework that utilizes a Graphics Processing Unit (GPU) for solving both flow and adjoint equations. It is built based on a GPU-accelerated flow solver that has been developed previously. Hence, the focus of this work is on how to solve the adjoint equations on the GPU and subsequently compute the gradients. The adjoint equations are right-preconditioned by a block Incomplete Lower Upper (ILU) preconditioner and solved by a restarted Generalized Minimum Residual (GMRES) method. The exact residual Jacobian matrix in the adjoint equations is computed using finite difference and a distance-2 graph coloring algorithm. With the adjoint-based gradients, the steepest descent method with momentum is employed for constrained aerodynamic shape optimization of a wing-body configuration at a transonic flow condition.