A coupled particle model with particle shifting technology for simulating transient viscoelastic fluid flow with free surface

Abstract

In this work, the decoupled finite particle coupled with smoothed particle hydrodynamics (DFP-SPH) method is firstly developed to simulate the viscoelastic fluid flow with free surface. A particle shifting technology is introduced to eliminate the tensile instability and nonuniformity of fluid particles. The motivations and embodiments include: (a) the partial derivatives of physical quantities of velocity, density and viscoelastic stress are calculated based on multivariate Taylor series and dominated contributions from diagonal matrices, which avoid the inversion of encountered ill-conditioned matrices potentially and improve the precision of numerical approximation to a certain extent; (b) a particle shifting technology is added to remove the tensile instability and nonuniformity of fluid particles in the frame of proposed DFP-SPH, and the determination of free surface particles is also proceeded in nature; (c) the dynamic boundary particles possessing computational simplicity are introduced and adopted in the proposed method. A moderate uniformization is proposed to eliminate the spatial effect of nonphysical boundary layers. Subsequently, the accuracy, consistency and convergence of present method are investigated on some benchmarks of Newtonian and Oldroyd-B fluids with analytical solutions. The validity of particle shifting technology in DFP-SPH is verified and multiple inter miscible viscoelastic drops impacting on the rigid wall are simulated and analyzed numerically for the capacity of proposed method. The procedure of jet bulking is well demonstrated through using Newtonian and Oldroyd-B models at different Weissenberg numbers, which possesses flexible free surfaces and tangled interfaces of multifluid layers. Numerical results show that the coupled particle model has a good performance on the viscoelastic fluid flow with free surface.