Accelerating Linearised Frequency-Domain Simulations for Unsteady Aerodynamics Using Vectorisation

The solution of large sparse linear systems of equations is ubiquitous when it comes to implicit computational fluid dynamics methods. Linear harmonic incarnations of non-linear time-steppers have become well established. One particularly useful application of such linear harmonic approaches is the computation of flutter boundaries, an important aspect in the design, analysis and certification of aircraft. Specifically, the unsteady aerodynamic response due to forcing in the structural modes of vibration is of interest. The curse of linearity requires the solution of the resulting linear system of equations for each structural mode (typically between 10 and 100) for multiple frequencies (typically around 10) and, exacerbating the computational burden, for multiple linearisation points. A similar simulation task in the aircraft design process arises from gust analysis. Usually, these linear systems are solved independently and one at a time, even though their underlying composition is closely related suggesting different approaches to acceleration. Our contribution explores acceleration with single instruction, multiple data parallel processing, which exploits the inherent data-level parallelism of the linear systems, activated using advanced vector extensions available on modern computing hardware. A state-of-the-art computational fluid dynamics solver has been upgraded accordingly, and the simultaneous solution of multiple linear systems is thoroughly studied.