A continuous adjoint method with objective function derivatives based on boundary integrals, for inviscid and viscous flows

An asynchronous metamodel-assisted memetic algorithm for CFD-based shape optimization

“…Its variation with respect to the design variable array, b ∈ R N , is expressed as follows, as in Papadimitriou and Giannakoglou (2007), The development of the field integrals of Equation (8), based on the Gauss divergence theorem, gives rise to…”

“…In general, the adjoint equations in discrete form can be derived through either the continuous, Pironneau (1974), Jameson (1988), Anderson and Venkatakrishnan (1997), Papadimitriou and Giannakoglou (2007, or the discrete adjoint approach, Elliot and Peraire (1996), Giles and Pierce (1997), Duta et al (2002). In the former, the adjoint equations are derived as p.d.e.…”

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

“…Aircraft configurations may be studied through multidisciplinary design optimization that takes into account both the flow and the structure [45,28,24]. The adjoint method has also extended to rotorcraft [29,12,30] and turbomachinery [56,34,57] design optimization.…”

Adjoint-Based Constrained Aerodynamic Shape Optimization for Multistage Turbomachines

“…Furthermore, Wu et al [19] calculated gradients based on the adjoint method and performed a constrained optimization of the VKI turbine stator in inviscid flow and the Standard Configuration 4 turbine stator in both laminar and turbulent flow. Papadimitriou and Giannakoglou [20,21] presented continuous and discrete adjoint formulations with objective function derivatives based only on boundary integrals and applied them to compressor and turbine blade design in two-and three-dimensional inviscid and viscous flows. Papadimitriou and Giannakoglou [22] also introduced a total pressure loss objective function to the continuous adjoint approach, which then was successfully minimized in compressor and turbine cascades while maintaining the flow turning and the blade thickness.…”

“…The red point is located at the centroid of the cell, while the six blue points represent the six flux faces. The transformation from the physical to the computational space is then defined by the metrics 20) for n, m = 1, 2, 3. Applying the mapping to the Navier-Stokes equations provides the field equations in computational space, where they read as…”