Smoothed particle hydrodynamics modeling of viscous liquid drop without tensile instability

Smoothed particle hydrodynamics (SPH), as a Lagrangian meshfree particle method, has been applied to modeling viscous liquid drop with surface tension and wetting dynamics. In the SPH model, the van der Waals (vdW) equation of state is usually used to describe the gas-to-liquid phase transition similar to that of a real fluid. However, the attractive forces between SPH particles originated from the cohesive pressure of the vdW equation of state can lead to tensile instability, which is associated with unphysical phenomena such as particle clustering or blowing away. This paper presents an improved SPH method for modeling viscous liquid drop. The inherent tensile instability in SPH is removed by using a hyperbolic-shaped kernel function which possesses non-negative second derivatives. A single-step approximation for heat flux is used in modeling viscous liquid drop with smoother temperature field. The formations of viscous liquid drops, both in 2D and 3D, are tested and it clearly demonstrates that the tensile instability can be effectively removed. The improved SPH method is also used to model two other numerical examples including the oscillation and binary collision of liquid drops without tensile instability.