A Time Domain Full Order Parallel Method for Turbomachinery Unsteady Flows

Abstract

In this study, the parallel inverted dual time stepping (PIDTS) method has been investigated for analyzing turbomachinery unsteady flows. This is the first known effort in exploiting temporal parallelization to reduce wall-clock time for analyzing turbomachinery unsteady flows in all time scales. This method relaxes the sequential time dependency of solutions at different time instants in the dual time stepping method to achieve parallel solutions at the expense of an increased number of pseudo-time iterations. To demonstrate its parallel scalability and solution stability and accuracy, a one-dimensional De Laval nozzle with a time-periodic back pressure disturbance has been used as a test case. Study indicates that the higher number of pseudo-time iterations is inevitable with a larger number of time instants marching together. A hybrid explicit and implicit method for accelerating solution convergence significantly mitigates the need for an increased number of pseudo-time iterations. Further verification and application have been conducted using a case of rotor-stator interaction of a transonic compressor stage. The obtained parallel efficiency is about 96%, 90%, 83%, 77%, and 72% with 2, 4, 8, 12, and 16 time instants marching together, respectively. The recommended number of time instants for parallelization is 2-10, which is a result of balancing parallel benefits, time consumption of additional pseudo-time iterations, and additional memory consumption. The obtained wall-clock speedup compared with the dual time stepping method is 1.9 to 3.5.