A distributed-memory MPI parallelization scheme for multi-domain incompressible SPH

A parallel scheme for a multi-domain truly incompressible smoothed particle hydrodynamics (SPH) approach is presented. The proposed method is developed for distributed-memory architectures through the Message Passing Interface (MPI) paradigm as communication between partitions. The proposal aims to overcome one of the main drawbacks of the SPH method, which is the high computational cost with respect to mesh-based methods, by coupling a multi-resolution approach with parallel computing techniques. The multi-domain approach aims to employ different resolutions by subdividing the computational domain into non-overlapping blocks separated by block interfaces. The particles belonging to different blocks are efficiently distributed among processors ensuring well balanced loads. The parallelization procedure handles particle exchanges both throughout the blocks and the competence domains of the processors. The matching of the velocity values between neighbouring blocks is obtained solving a system of interpolation equations at each block interfaces through a parallelized BiCGSTAB algorithm. Otherwise, a whole pseudo-pressure system is solved in parallel considering the Pressure Poisson equations of the fluid particles of all the blocks and the interpolation equations of all the block interfaces. The employed test cases show the strong reduction of the computational efforts of the SPH method thanks to the interaction of the employed multi-resolution approach and the proposed parallel algorithms.