A SPH-based particle method for simulating 3D transient free surface flows of branched polymer melts

In this article we present a particle method based on smoothed particle hydrodynamics (SPH) for simulating three-dimensional (3D) transient free surface flows of branched polymer melts which are governed by the single equation version of the eXtended Pom-Pom (XPP) model. In order to remedy the so-called tensile instability which results in particle clustering and unphysical fracture in the state of fluid stretching, both artificial stress and artificial viscosity are incorporated into the momentum equation. For facilitating the implementation of the wall boundary condition in 3D space, an enhanced treatment of solid boundaries is proposed in this paper. The proposed SPH algorithm is validated by the excellent agreement between the numerical and the analytical solutions of Hagen-Poiseuille flow of an Oldroyd-B fluid. To demonstrate the ability of the numerical method in simulating free surface flows of branched polymer melts, the fall and impact on a rigid plate of a XPP fluid droplet is investigated for a wide range of the relevant parameters. Specifically, the convergence of the numerical results is discussed by three particle sizes of different levels of refinement. To provide some additional applications of 3D free surface flows of branched polymer melts, the challenging jet buckling and rod-climbing effect of viscoelastic fluids are further simulated and analyzed. All numerical results establish the capability of the SPH-based particle method to simulate 3D transient free surface flows of branched polymer melts in an entirely mesh-free framework.