A High-Fidelity Framework Approach Enabling High-order Implicit Time Stepping For MDAO

Abstract

In order to allow high-order time integration of multidisciplinary scenarios via a framework-based approach, we developed RKOpenMDAO. It is an extension to the base-line version of the OpenMDAO framework - which is primarily designed for steady-state like MDAO applications - and enables multidisciplinary time integration via diagonally implicit Runge–Kutta (DIRK) schemes. To yield a robust framework approach capable of time-resolved high-fidelity MDAO, the approach offers strong, nested solution schemes to solve the coupled multidisciplinary systems that arise per time step/stage of the implicit time integration. The implementation is described for the OpenMDAO framework which is used in conjunction with FlowSimulator HPC environment. The verification and demonstration cases presented in the paper benefit from a seamless and modular integration of the CFD solver library CODA behind a unified component/plugin API, which provides access to methods for disciplinary block inversions, residual computations and the calculation of the corresponding derivatives by means of algorithmic differentiation. Numerical experiments are shown for Kaps' problem, a 2D NACA0012 airfoil coupled with a torsion spring, and the ONERA-M6 wing in fully-turbulent flow executed in an MPI-parallel way. We demonstrate that the design order of the high-order Runge–Kutta time integration can be retained for high-fidelity multiphysics problems.