Abstract

The design of next generation aircraft will rely on the use of high-fidelity computational fluid dynamics (CFD). For this purpose, the Paired Explicit Runge-Kutta (P-ERK) time stepping method was developed. It is a variation of explicit Runge-Kutta methods that allows the pairing of multiple methods within a given simulation. This results in higher stability methods being used in stiff regions, and lower cost methods being used in non-stiff regions, resulting in significant performance improvements. This work explores the utility of Graphical Processing Unit (GPU) acceleration combined with P-ERK schemes Subcritical flow over a smooth sphere at a Reynolds number (Re) of 3700 was used as the validation case. The flux reconstruction (FR) spatial discretization scheme was used with the implicit Large Eddy Simulation (ILES) turbulence modelling approach. Instantaneous quantities such as velocity fluctuations, Strouhal numbers, and time-averaged quantities such as drag coefficient, pressure coefficient, back pressure ratio, and Reynolds stresses were obtained. In addition, Q-criterion contours were generated and used to obtain separation angle and recirculation bubble length. This study shows that the P-ERK method can achieve good agreement with both reference simulation, and experimental data. Moreover, when compared to the traditional fourth order Runge-Kutta (RK) method the P-ERK scheme shows an average speedup factor of 4.73 using GPUs and of 5.82 using CPUs with regards to solution polynomial scaling, and with regards to resource scaling it requires approximately 8 times more resources using CPUs, or each CPU has an approximately 45 times greater runtime compared to one GPU. This is a significant reduction in computational times, while maintaining accuracy.