TITLE:
SPH Particle Collisions for the Reduction of Particle Clustering, Interface Stabilisation and Wall Modelling
AUTHORS:
Arno Kruisbrink, Stan Korzilius, Frazer Pearce, Hervé Morvan
KEYWORDS:
SPH, Particle Clustering, Multiphase Flow, Interface Stabilisation, Wall Modelling
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.9,
September
18,
2018
ABSTRACT: The pair-wise forces in the SPH momentum equation
guarantee the conservation of momentum, but they cannot prevent particle
clustering and wall penetration. Particle clustering may occur for several
reasons. A fundamental issue is the tensile instability, which is caused by
negative numerical pressures. Clustering may also occur due to certain
properties of the kernel gradient. Discontinuities in the pressure and its
gradient, due to surface tension and gravity, may cause particle instabilities
near the interface between two fluids. Wall penetration is also a form of
particle clustering. In this paper the particle collision concept is introduced
to suppress particle clustering. Here, the use of kinematic conditions (motion)
rather than dynamic conditions (forces) is explored. These kinematic conditions
are obtained from kinetic collision theory. Conservation of momentum is
maintained, and under elastic conditions conservation of energy as well. The
particle collision model only becomes active when needed. It may be seen as a
particle shifting method, in the sense that the velocities are changed, and as
a consequence of that the particle positions change. It is demonstrated in
several case studies that the particle collision model allows for realistic
(low) viscosities. It was also found to stabilise the interface between two
fluids up to high, realistic density ratios (1000:1) in typical liquid-gas
applications. As such it can be used as a multi-fluid model. The concept allows
for real wave speed ratios (and far beyond), which, as well as real viscosities, are essential in the modelling of heat transfer applications. The collisions
with walls allow for no-slip conditions at real viscosities while wall
penetration is suppressed. In summary, the particle collision model makes SPH
more robust for engineering.