Algorithmic Differentiation Framework of the CFD Software by ONERA, DLR, Airbus (CODA): Design and Evaluation for Adjoint Sensitivity Analysis of Aircraft

In this paper, we present the Algorithmic Differentiation (AD) framework of the CFD software by ONERA, DLR, and Airbus (CODA). The focus is on the reverse-mode differentiation capabilities of the CFD library CODA that are required for large-scale adjoint sensitivity analyses. Particular attention is given to four key aspects: 1) The AD framework allows the application of AD libraries based on operator overloading on the level of face and element operations in a compact differentiation approach for the differentiation of the residual function. The approach retains key HPC capabilities of the primal CFD method such as overlapping communication and computation in conjunction with adjoint computations by reverse-mode AD, leveraging distributed memory, shared memory and SIMD/vector parallelism. 2) An AD abstraction layer is defined in the CFD software for interoperability with different AD libraries available with their individual advantages, license conditions and tape strategies for reverse-mode AD. 3) A unified programming interface is provided that systematically offers entry points for both forward and reverse-mode AD capabilities of (explicit) functions and implicit operations of the CFD software CODA. A derivative-enabled Python-interface called FSMDAO allows calling the CFD library with granular access to exact forward and reverse differentiation of the CFD modules in combination with state-of-the-art MDAO frameworks. 4) For an efficient and robust processing of large-scale adjoint computations, nested stacks of solvers and preconditioners can be built with both matrix-based and matrix-free (transposed) linearized solver operations in the hierarchical solution process. Numerical experiments are presented to evaluate and assess the properties of the adjoint complement of the CFD software CODA on the way to multidisciplinary design optimizations on large scale. Solver convergence is investigated based on the powered DLR-F25 aircraft configuration in steady-state RANS flow using different linear solver stacks in the implicit solution process. In a strong parallel scalability study, linear scaling of time-to-solution is observed down to less than 10 thousand degrees of freedom per CPU core. Weak scalability is studied for the CRM/DPW5 wing-body configuration using an unstructured mesh sequence with 18 million to 1.2 billion degrees of freedom, showing a relative run-time increase of less than 10 percent on the large mesh compared to the coarse mesh.