Stabilization of a Time‐Dependent Discrete Adjoint Solver for Chaotic Incompressible Flows.

Following the growth of computational fluid dynamics in engineering applications, adjoint methods for sensitivity analysis are being applied to an increasing range of industrial problems. In recent years, growth in computational power has led to widespread use of high‐fidelity, time‐resolved techniques, such as large‐eddy simulation, for applications, including bluff‐body aerodynamics, where time‐averaged equations may be less reliable. The solution of time‐dependent adjoint equations, however, becomes unstable in time as the Reynolds number increases and the flow becomes chaotic. The source of this instability has been explained by analysis of the system's Lyapunov exponents and several solutions have been proposed in the literature based on least‐squares shadowing. Currently, such techniques impose a higher computational cost compared to classical adjoint methods and may become infeasible when the number of unstable Lyapunov exponents is large. In this work, we explore a more recently proposed approach, which balances the adjoint energy source term with added artificial dissipation. The stability of this approach is investigated for a discrete adjoint solver based on the time‐dependent incompressible Navier‐Stokes equations. The accuracy of the resulting shape sensitivities is analyzed using a linear regression technique for the flow around a circular cylinder. [ABSTRACT FROM AUTHOR]