A parallel inverted dual time stepping method for unsteady incompressible fluid flow and heat transfer problems

Abstract

The simulation of unsteady incompressible fluid flow and heat transfer problems is a huge time-consuming task and has been becoming one of the hottest topics in the fields of computational fluid dynamics and numerical heat transfer. Pure spatial parallelization has been so far the most widely used parallel strategy to speed up unsteady simulations but suffers from the problem of speedup saturation as parallel scale increases. In order to further speed up unsteady simulations and exploit the concurrency in temporal dimension, we propose a novel temporal parallelization strategy, i.e., parallel inverted dual time stepping method, by simply inverting the sequence of the inner loop (pseudo time) and the outer loop (physical time) within the dual time stepping framework. The parallel performance of the proposed method is verified and validated with three steady/unsteady problems. Parallel results of the proposed method agree well with those of the dual time stepping method and the available benchmark solutions. The parallel efficiency of the proposed method is about 96%, 81%, 62%, 51%, 45% for 4, 8, 12, 16, 20 CPU cores, respectively, which is considerably higher than that of the widely used parareal method. The proposed method has potential in further increasing parallel scale as spatial parallelization is saturated.