In this paper, we present the application of the GPU-based particle simulation to Three-dimensional (3D) complicated fluid flow problems including free surfaces with surface tension and drag force. The particle approach is based on the SPH (Smoothed Particle Hydrodynamics) method using quintic spline kernel functions. We adopt the inter-particle potential force model with a potential coefficient as a surface tension model. The GPU-implementation consists of the search for neighboring particles in the locally uniform grid cell using hash function. Numerical results demonstrate the workability and validity of the present approach through the dam-breaking flow problem, the droplet oscillation and the droplet-falling impact with surface tension and drag force.
The numerical simulations of three-dimensional (3D) viscous fluid flows including multi-scale/physics and moving boundary/obstacle are indispensable in science and engineering fields from a practical point of view. Numerical difficulties have been experienced in the solution of the Navier-Stokes equations at higher Reynolds numbers. In particular, it is well known that the centered finite difference and standard Galerkin finite element formulations lead to spurious oscillatory solutions for flow problem at high Reynolds number regimes. To overcome such spurious oscillations, various upwind/upstream-based schemes have been significantly presented by many researchers in both frameworks. On the other hand, there are various gridless/meshless-based particle methods, such as SPH (Smoothed Particle Hydrodynamics) method (Gingold and Monaghan, 1977; Lucy, 1977), and MPS (Moving Particle Semi-implicit) one (Koshizuka and Oka, 1996; Khayyer and Gotoh, 2009; Khayyer and Gotoh, 2016) to simulate effectively such complicated flow problems.
Recently, the physics-based computer simulations on the GPU (Graphics Processing Units) (Harada et al., 2008; Green, 2010; Hori et al., 2011) have increasingly become an important strategy for solving efficiently various problems, such as fluid dynamics, solid dynamics, and so forth. In our previous work, we have presented a GPU-based MPS scheme using logarithmic weighting function for solving effectively 2D/3D problems of incompressible fluid flow (Kakuda et al., 2012).
