Computation of the Adjoint Navier-Stokes Equations using the Discontinuous Galerkin
Please login to view abstract download link
We present an approach based on the discontinuous Galerkin method to approximate the solution of the steady and unsteady adjoint Navier-Stokes equations for incompressible fluids. The adjoint Navier-Stokes equations occur in shape optimization and other optimal control problems with fluid dynamics applications. A widely used discretization technique is the finite volume method (FVM) to approximate the physical state, particularly when considering turbulent flows with high Reynolds numbers. When computing the adjoint equations, non-conservative terms occur. The FVM requires treating non-conservative terms explicitly, decelerating and destabilizing the procedure. In practice, however, the occurring terms are neglected, leading to an inconsistent adjoint state. Using the more flexible discontinuous Galerkin method and an inexact Schur complement preconditioner for spatial discretization allows for treating non-conservative terms implicitly. Our approach aims to compute a consistent adjoint state and gain robustness of the solution procedure. It is applied to different shape optimization examples aiming for the drag minimization of an obstacle object.
