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For flows with strong periodic content, time-spectral methods can be used to obtain time-accurate solutions at substantially reduced cost compared to traditional time-implicit methods which operate directly in the time domain. In their original form, time spectral methods are applicable only to purely periodic problems and formulated for single grid systems. A wide class of problems involve quasi-periodic flows, such as maneuvering rotorcraft problems, where a slow transient is superimposed over a more rapid periodic motion. Additionally, the most common approach for simulating combined rotor-fuselage interactions is through the use of a dynamically overlapping mesh system. Thus, in order to represent a practical approach for rotorcraft simulations, time spectral methods that are applicable to quasi-periodic problems and capable of operating on overlapping mesh systems need to be formulated. In this paper, we propose separately an extension of time spectral methods to quasi-periodic problems, and an extension for overlapping mesh configurations. In both cases, the basic implementation allows for two levels of parallelism, one in the spatial dimension, and another in the time-spectral dimension, and is implemented in a modular fashion that minimizes the modifications required to an existing steady-state solver. Results are given for three-dimensional quasi-periodic problems on a single mesh, and for two-dimensional periodic overlapping mesh systems.

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