On the stabilization of steady continuous adjoint solvers in the presence of unsteadiness, in shape optimization.

Skamagkis, Themistoklis; Papoutsis‐Kiachagias, Evangelos M.; Giannakoglou, Kyriakos C.

Adjoint‐based shape optimization using unsteady solvers is costly and/or memory demanding. When mild unsteadiness is present or the flow in/around the optimized shape is not expected to be time‐varying, steady primal and adjoint solvers can be used instead. However, in such a case, convergence difficulties caused by flow unsteadiness must properly be treated. In this article, the steady primal and the corresponding (continuous) adjoint solvers are both stabilized by implementing the recursive projection method (RPM). This is carried out in the adjointOptimisation library of OpenFOAM, developed, and made publicly available by the group of authors. Upon completion of the optimization using steady solvers, unsteady re‐evaluations of the optimized solutions confirm a reduction in the time‐averaged objective function. In complex cases, in which the RPM may not necessarily ensure convergence of the adjoint solver on its own, the controlled damping of the adjoint transposed‐convection (ATC) term is additionally implemented. This is demonstrated in the shape optimization of a motorbike fairing where averaged primal fields over a number of iterations of the steady flow solver are used for the solution of the adjoint equations. Cases in which the RPM is, on its own, sufficient in ensuring convergence of the adjoint solver are additionally studied by using a controlled ATC damping, to assess its impact on the computed sensitivity derivatives. Comparisons show that controlled/mild ATC damping is harmless and greatly contributes to robustness.

STRUCTURAL optimization; ADJOINT differential equations; MOTORCYCLES

International Journal for Numerical Methods in Fluids, 2021, Vol 93, Issue 8, p2677

0271-2091

Academic Journal

10.1002/fld.4993