Unsteady adjoint analysis for output sensitivity and mesh adaptation

[摘要] Adjoint analysis in computational fluid dynamics (CFD) has been applied to design optimization and mesh adaptation, but due to the relative expense of unsteady analysis these applications have predominantly been for steady problems. As the use of adjoint methods continues to becomes more prevalent, more problems are encountered for which steady analysis may not be appropriate. This thesis examines three aspects of unsteady adjoint analysis. First, this work investigates problems exhibiting small-scale output unsteadiness when solved with time-inaccurate iterative solvers. It is demonstrated that unconverged steady flow calculations, even with small output unsteadiness, can lead to significant variability in the estimated output sensitivity due to the arbitrary choice of unconverged state upon which the linearization is performed. Further, time-inaccurate ;;unsteady;; iterative solutions depend on the iterative method used and may exhibit different output and output sensitivity compared to the steady flow or time-accurate unsteady flow. With the motivation for unsteady simulation established, output and output parameter sensitivities of periodic unsteady problems are sought using finite-time averaging. Periodic outputs computed over a finite time span are found to converge slowly and output sensitivities may be nonconvergent when the period of oscillation is a function of the parameter of interest. A theoretical basis for this lack of convergence is identified and output windowing is proposed to alleviate its effect. Output windowing is shown to enable the accurate computation of periodic output sensitivities and to decrease simulation time to compute periodic outputs and sensitivities. Finally, a spatial mesh adaptation approach is developed for unsteady wake problems and other problems with smooth and persistent regions of unsteadiness. For this class of problems, a higher-order discretization coupled with a single spatial mesh approach is appropriate to capture both steady and unsteady regions. The method proposed herein extends the anisotropic, output-based Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm of Yano and Darmofal to optimize the spatial mesh driven by an unsteady flow field.

[发布机构] Massachusetts Institute of Technology