A numerical study of the SPH method for simulating transient viscoelastic free surface flows

The smoothed particle hydrodynamics (SPH) method is extended and tested for the numerical simulation of transient viscoelastic free surface flows. The basic equations governing the free surface flow of an Oldroyd-B fluid are considered and approximated by SPH. In particular, a drop of an Oldroyd-B fluid impacting a rigid plate is simulated. Results for a Newtonian fluid are also presented for comparison. It is found that the original SPH method, which has been successfully applied to the simulation of transient viscoelastic flows in bounded domains (such as the start-up flow between parallel plates), is unable to simulate the viscoelastic free surface flow considered here because of the so-called tensile instability. This instability leads to unrealistic fracture and particle clustering in fluid stretching and may eventually result in complete blowup of the simulation. Recent works have shown that in simulations of elastic solids the tensile instability can be removed by an artificial stress. Here we show that the same idea also works for viscoelastic fluids provided that the constant parameter entering in the definition of the artificial stress is properly chosen. Numerical results obtained are in good agreement with those simulated by a finite difference technique.