GPU acceleration of multigrid preconditioned conjugate gradient solver on block-structured Cartesian grid

Onodera, Naoyuki   ; Idomura, Yasuhiro   ; Hasegawa, Yuta   ; Yamashita, Susumu   ; Shimokawabe, Takashi*; Aoki, Takayuki*

We develop a multigrid preconditioned conjugate gradient (MG-CG) solver for the pressure Poisson equation in a two-phase flow CFD code JUPITER. The MG preconditioner is constructed based on the geometric MG method with a three-stage V-cycle, and a RB-SOR smoother and its variant with cache-reuse optimization (CR-SOR) are applied at each stage. The numerical experiments are conducted for two-phase flows in a fuel bundle of a nuclear reactor. The MG-CG solvers with the RB-SOR and CR-SOR smoothers reduce the number of iterations to less than 15% and 9% of the original preconditioned CG method, leading to 3.1- and 5.9-times speedups, respectively. The obtained performance indicates that the MG-CG solver designed for the block-structured grid is highly efficient and enables large-scale simulations of two-phase flows on GPU based supercomputers.