A Reduced Order Cyclic Method for Computation of Limit Cycles

A reduced order cyclic method was developed to compute limit-cycle oscillations for large, nonlinear, multidisciplinary systems of equations. Method efficacy was demonstrated for two simplified models: a typical-section airfoil with nonlinear structural coupling and a nonlinear panel in high-speed flow. The cyclic method was verified to maintain second-order temporal accuracy, yield converged limit cycles in about 10 Newton iterates, and provide precise estimates of cycle frequency. This method was projected onto a low-order space using a set of variables governing the amplitudes of empirically derived modes, which were computed with the proper orthogonal decomposition. In this reduced order form, the cyclic Jacobian was greatly compressed, allowing accurate limit cycle solutions to be very efficiently computed.The U.S. Governments right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged.