BibTeX
@ARTICLE{
         Kenway2019Eaa,
       title = "Effective adjoint approaches for computational fluid dynamics",
       journal = "Progress in Aerospace Sciences",
       volume = "110",
       pages = "100542",
       year = "2019",
       issn = "0376-0421",
       doi = "10.1016/j.paerosci.2019.05.002",
       url = "https://www.sciencedirect.com/science/article/pii/S0376042119300120",
       author = "Kenway, Gaetan K. W. and Mader, Charles A. and He, Ping and Martins, Joaquim R.R.A.",
       keywords = "Adjoint methods, Computational fluid dynamics, Sensitivity analysis, Algorithmic
         differentiation, Discrete adjoint benchmarks, Aerodynamic shape optimization",
       abstract = "The adjoint method is used for high-fidelity aerodynamic shape optimization and is
         an efficient approach for computing the derivatives of a function of interest with respect to a
         large number of design variables. Over the past few decades, various approaches have been used to
         implement the adjoint method in computational fluid dynamics solvers. However, further advances in
         the field are hindered by the lack of performance assessments that compare the various adjoint
         implementations. Therefore, we propose open benchmarks and report a comprehensive evaluation of the
         various approaches to adjoint implementation. We also make recommendations on effective approaches,
         that is, approaches that are efficient, accurate, and have a low implementation cost. We focus on
         the discrete adjoint method and describe adjoint implementations for two computational fluid
         dynamics solvers by using various methods for computing the partial derivatives in the adjoint
         equations and for solving those equations. Both source code transformation and operator-overloading
         algorithmic differentiation tools are used to compute the partial derivatives, along with finite
         differencing. We also examine the use of explicit Jacobian and Jacobian-free solution methods. We
         quantitatively evaluate the speed, scalability, memory usage, and accuracy of the various
         implementations by running cases that cover a wide range of Mach numbers, Reynolds numbers, mesh
         topologies, mesh sizes, and number of CPU cores. We conclude that the Jacobian-free method using
         source code transformation algorithmic differentiation to compute the partial derivatives is the
         best option because it computes exact derivatives with the lowest CPU time and the lowest memory
         requirements, and it also scales well up to 10 million cells and over one thousand CPU cores. The
         superior performance of this approach is primarily due to its Jacobian-free adjoint strategy. The
         cases presented herein are publicly available and represent platform-independent benchmarks for
         comparing other current and future adjoint implementations. Our results and discussion provide a
         guide for discrete adjoint implementations, not only for computational fluid dynamics but also for a
         wide range of other partial differential equation solvers.",
       ad_area = "Aerodynamics"
}