A comparison of optimization-based approaches for a model computational aerodynamics design problem
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Analysis of finite-volume discrete adjoint fields for two-dimensional compressible Euler flows
2022, Journal of Computational PhysicsCitation Excerpt :Discrete and continuous adjoint methods are well established methods to efficiently calculate derivatives of aerodynamic functions with respect to numerous design parameters. Adjoint-based derivatives and adjoint-fields are commonly used for local shape optimization [2–6], goal-oriented mesh adaptation [7–14], flow control [15,16], meta-modelling [17], receptivity-sensitivity-stability analyses [18], and data assimilation [19]. These methods are often used for the linear analysis of non-linear conservation laws where the adjoint is defined as the dual to the linearized equations around a given solution to the direct non-linear problem.
Discrete adjoint of fractional-step incompressible Navier-Stokes solver in curvilinear coordinates and application to data assimilation
2019, Journal of Computational PhysicsCitation Excerpt :The boundary conditions for the discrete adjoint equations are straightforward to derive and implement, compared to those of the continuous variant. Since the first application for quasi-one-dimensional compressible Euler equations [19], this approach has been developed for more complex problems. For example, Mani & Mavriplis derived the discrete adjoint of unsteady compressible Euler equations with deforming meshes [20]; Nielsen et al. extended the formulation to three-dimensional unsteady compressible RANS equations on overset grids [21]; de Pando et al. developed adjoint operators for the linearized Navier-Stokes solvers which are generated by an efficient algorithm that they proposed [22].
State-of-the-art in aerodynamic shape optimisation methods
2018, Applied Soft Computing JournalCitation Excerpt :The adjoint form of the sensitivity information is particularly efficient for aerodynamic optimisation applications as the number of cost functions (outputs) is small, while the number of design variables (inputs) is relatively larger. The discrete adjoint method (as opposed to continuous adjoint method) is generally favoured in aerospace-based optimisation as it ensures that sensitivities are exact with respect to the discretised objective function [81,82]. The implementation of the adjoint method for the governing equations of the flow analysis can often be difficult to derive and require direct manipulation; adjoint methods require much more involved detailed knowledge of the computational domain.
Dual consistency and functional accuracy: A finite-difference perspective
2014, Journal of Computational PhysicsCitation Excerpt :In the continuous-adjoint approach, associated with Jamesonʼs pioneering work in aerodynamic shape optimization [4], the adjoint PDE is first derived from the primal3 PDE and functional; subsequently, the primal and adjoint PDEs are discretized independently. In the discrete-adjoint approach, see e.g. [16,17], the discretized primal PDE and functional are used to derive the linear system for the adjoint variables. In the PDE-constrained optimization literature, the discrete-adjoint approach (resp.
Numerical sensitivity analysis for aerodynamic optimization: A survey of approaches
2010, Computers and Fluids