Numerical simulation of 3D-unsteady viscoelastic free surface flows by improved smoothed particle hydrodynamics method

摘要

In this paper, a working smoothed particle hydrodynamics (SPH) method is introduced to solve three-dimensional (3D) transient viscoelastic flows with complex free surfaces. In order to alleviate the unphysical behavior of fracture and particle clustering in fluid stretching which is the so-called tensile instability, an artificial stress term is incorporated into the momentum equation. To facilitate the enforcement of 3D wall boundaries, a new boundary treatment technique, which can observably improve the computational efficiency, is proposed. The proposed SPH method is validated by solving the Hagen-Poiseuille flow of an Oldroyd-B fluid and comparing the SPH results with the available analytical solutions. Two challenging fluid flow problems, namely, a viscoelastic drop impacting on a rigid plate and jet buckling, are simulated to demonstrate the capability of the proposed SPH method in handing 3D viscoelastic free surface flows. Results for a Newtonian fluid are also shown for comparison. All numerical results obtained are in agreement with the available data.