High-Order Multidisciplinary Time Integration Towards Adaptive Time Stepping

Abstract

The aim of this work is to carry over adaptive higher-order time-stepping techniques - well-known and established for example in the context of single-disciplinary (CFD) time integration - to multidisciplinary design analysis and optimization (MDAO). To this end, an MDAO framework extension built on OpenMDAO, RKOpenMDAO, was developed to allow for time-accurate multidisciplinary high-order time integration. RKOpenMDAO provides MDAO framework capabilities - such as multidisciplinary gradient-accumulation and monolithic nested solution techniques - usually known from steady-state type MDAO scenarios for multidisciplinary implicit time integration. It was enabled for adaptive time stepping in this work. The multidisciplinary error in time is estimated by means of embedded Runge–Kutta schemes. The new-generation CFD Software by ONERA, DLR and Airbus (CODA) was modularly integrated into the suggested MDAO framework approach for multidisciplinary, adaptive time-stepping in a time-accurate way. Numerical experiments were carried out for an elementary unsteady aeroelastic case of a NACA0012 section in compressible Euler flow coupled to a torsional spring. With the MDAO-framework approach we could show that (a) advanced implicit solution capabilities with nested multidisciplinary solvers can be used on the level of the monolithic multidisciplinary system, (b) a computationally efficient error estimator based on embedded Runge-Kutta methods is able to successfully drive the adaptive time-step control, (c) the targeted temporal accuracy can be achieved by effectively adjusting the time-step, and (d) the suggested MDAO-framework extension, RKOpenMDAO, is applicable for multiphysics analyses with high-fidelity simulation components.