Abstract: At the beginning of the talk we discuss how to set up robust adjoint solvers for optimization and control in fluid mechanics in an automated fashion by the advanced use of algorithmic differentiation (AD). Then we discuss how to extend the resulting fixed-point solvers into so-called one-shot methods, where one solves the optimality system consisting of the primal, the dual/ adjoint and the design equations simultaneously. This is discussed for steady state cases first and then extended to unsteady partial differential equations (PDEs).  Integrating existing solvers for unsteady PDEs into a simultaneous optimization method is challenging. Especially in the presence of chaotic and turbulent flow, solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length. The new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations. This enables efficient one-shot optimization that is independent of the time domain length, even in the presence of chaos.

SCC-Seminare und Kolloquien