An Efficient Flexible GMRES Solver for the Fully-coupled Time-spectral Aeroelastic System

Abstract

The time-spectral (TS) method applied to the coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with TS methods over traditional time-implicit methods hinges on the ability to rapidly solve the large non-linear system resulting from TS discretizations which become larger and stiffer as more time instances are employed. An ideal time-spectral solver would scale linearly, such that a doubling of the number of time-instances used would double the wall-clock time needed to converge the solution on the same computational hardware. The present work is focused on achieving an optimal solver for large numbers of time instances. In order to increase the efficiency of the solver, and to improve robustness particularly for large numbers of time instances and fluid/structure coupling, TS methods are reworked such that the Generalized Minimal Residual Method (GMRES) is used to solve the implicitly coupled, time-spectral, fluid/structure linear system over all time instances at each non-linear iteration. The use of GMRES as the linear solver makes these methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods.