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.
Highlights
Smoothed particle hydrodynamics (SPH) is a numerical, Lagrangian method to simulate fluid flows
The pair-wise forces in the SPH momentum equation guarantee the conservation of momentum, but they cannot prevent particle clustering and wall penetration
The use of kinematic conditions rather than dynamic conditions is explored. These kinematic conditions are obtained from kinetic collision theory
Summary
Smoothed particle hydrodynamics (SPH) is a numerical, Lagrangian method to simulate fluid flows. The vanishing repelling force is the result of the flat shape of most commonly used kernels for inter-particle distances close to zero. This implies that for very small distances the kernel gradient tends to zero and as a consequence the (repulsive) pressure force vanishes. Remeshing as described by Chaniotis et al [12] prevents particles from clustering, but it has disadvantages as well It implies interpolation, which affects the accuracy and makes it computationally expensive. With remeshing SPH loses one of its biggest advantages: not having a predefined mesh Another remedy for the vanishing repelling force is a convex kernel function that does not have a flat central portion. Such kernels have been introduced by, e.g. Schussler and Schmitt [13]; Johnson and Beissel [14]; Read et
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