Multirate time-stepping least squares shadowing method

Abstract

The recently developed least squares shadowing (LSS) method reformulates unsteady turbulent flow simulations to be well-conditioned time-domain boundary-value problems. We see from Wang et al. (2013) that the reformulation from LSS can enable scalable parallel in-time simulation of turbulent flows. It utilizes the large number of processors in high-performance machines in order to find a trajectory that satisfies the given governing equation effectively by relaxing the initial condition. This method can speed up the wall clock time of finding the solution by effectively parallelizing in the temporal domain as well as the spatial domain. However, the traditional LSS method was limited by the smallest time-step of the entire domain, and thus required solving of extremely large block tri-diagonal systems.

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