We developed a practical technique for calculating pressures and pressure gradients for the moving particle semi-implicit (MPS) method. Specifically, a new free-surface boundary condition for the pressure Poisson equation was developed by assuming that there are virtual particles over the surface. We treat the pressure of the virtual particles as a known value. A single liquid-phase flow is simulated taking into account the pressure of these virtual particles. A technique for detecting surface particles also was developed and used for accurately imposing the free-surface boundary condition. The pressure gradient model was modified to mitigate particle clustering and a single-layer wall model was developed to reduce the number of wall particles. We applied our technique to several problems, verifying that virtual surface particles suppress pressure oscillations and particle clusterings. The technique enables reliable differences in free-surface pressures to be taken and simulates instances of lower fluid pressure than that of a free surface.

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In the present study, performance improvements of the particle search and particle interaction calculation steps constituting the performance bottleneck in the moving particle simulation method are achieved by developing GPU-compatible algorithms for many core processor architectures. In the improvements of particle search, bucket loops of the cell-linked list are changed to a loop structure having fewer local variables and the linked list and the forward star of particle search algorithms within a bucket are compared. In the particle interaction calculation, the problem of the ratio of particles within the interaction domain to the neighboring particle candidates being quite low is improved. By these improvements, a performance efficiency of 24.7 % can be achieved for the first-order polynomial approximation scheme using NVIDIA Tesla K20, CUDA-6.5, and doubleprecision floating-point operations.

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