A coupled discrete adjoint method for optimal design with dynamic non-linear fluid structure interactions

Abstract

Incorporating high-fidelity analysis methods in multidisciplinary design optimization necessitates efficient sensitivity evaluation, which is particularly important for time-accurate problems. This thesis presents a new discrete adjoint formulation suitable for fully coupled, non-linear, dynamic FSI problems. The solution includes time-dependent adjoint variables that arise from grid motion and chosen time integration methods for both the fluid and structural domains. Implemented as a generic multizone discrete adjoint solver for time-accurate analysis in the open-source multiphysics solver SU2, this provides a flexible framework for a wide range of applications. Design optimization of aerodynamic structures need accurate characterization of the coupled fluid-structure interactions (FSI). Incorporating high-fidelity analysis methods in the multidisciplinary design optimization (MDO) necessitates efficient sensitivity evaluation, which is particularly important for time-accurate problems. Adjoint methods are well established for sensitivity analysis when large number of design variables are needed. The use of discrete adjoint method through algorithmic differentiation enables the evaluation of sensitivities using an approximation of the Jacobian of the coupled problem, thus enabling this approach to be applied for multidisciplinary analysis. This thesis presents a new discrete adjoint formulation suitable for fully coupled, non-linear, dynamic FSI problems. A partitioned approach is considered with finite volume for the fluid and finite elements for the solid domains. The solution includes the time-dependent adjoint variables that arise from the grid motion and chosen time integration methods for both the fluid and structural domains. Implemented as a generic multizone discrete adjoint solver for timeaccurate analysis in the open-source multiphysics solver SU2, this provides a flexible framework for a wide range of applications. The partitioned FSI solver approach has been leveraged to extend the dynamic FSI capabilities to low speed flows through the introduction of a densitybased unsteady incompressible flow solver. The developed methodology and implementation are demonstrated using a range of numerical test cases. Optimal design for steady, coupled FSI problems are firstly presented before moving to the building blocks of dynamic coupled problems using single domain analysis, for both structural and fluid domains in turn. The new unsteady incompressible fluid solver, for both the primal and adjoint analysis, are verified against a range of well-known benchmark test cases, including problems with grid motion. Finally, applications of coupled dynamic problems are presented to verify both the unsteady incompressible solver for FSI as well as the successful verification of the discrete adjoint sensitivities for the transient response of a transonic compliant airfoil for a variety of both aerodynamic and structural objective functions.