Evaluation of CFD-Coupled Adaptive Time-Stepping for Time-Accurate MDA(O)
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In this work we present an adaptive time-stepping approach that was implemented in a framework environment for multidisciplinary design analysis and optimization (MDAO), based on the open-source MDAO framework OpenMDAO [1, 3]. The baseline framework approach for large MDAO computations in steady-state conditions is MPI-parallel from end-to-end. It offers exact sensitivity derivatives obtained from algorithmic differentiation (AD). The framework was extended to carry out multidisciplinary time-stepping via (diagonally) implicit Runge-Kutta methods ([D]IRK) according to the method of lines. To this end, a time-integrator, RKOpenMDAO, was developed in previous work [1] enabling OpenMDAO for coupled analyses and optimizations for computations the time domain. The steady-state MDAO-framework capabilities are retained. By means of high-order accuracy in time, embedded error estimators can now be used for the analysis of time-dependent multidisciplinary problems, including the capability for adaptive time stepping. Adaptive time stepping allows to reach a predefined error tolerance while keeping computational work low compared to a homogeneous time stepping scheme. A feasibility study was presented by Shuvi et al. [2]. In this work, the adaptive time-stepping approach is studied for selected computational cases of different complexity levels: among them are aerodynamic 2D and 3D problems in inviscid flow, laminar and fully-turbulent URANS flow, simulated by including the CFD Software by ONERA, DLR and Airbus (CODA) [4] into the framework. The adaptive time-stepping will be investigated for CFD-only cases followed by CFD-coupled configurations, e.g. by attaching the wings/aircraft to a (torsional) spring. We intend to consider time-integration – including convergence against the steady-state equilibrium – and gust-encounter scenarios of airfoils and aircraft. In the presentation, the results will be discussed and assessed in terms of time accuracy, computational efficiency, robustness and automation level. An outlook will be provided regarding the potential and challenges for large-scale, gradient-based MDAO.
