SPH simulations of three-dimensional non-Newtonian free surface flows

In this paper, the smoothed particle hydrodynamics (SPH) method is extended to deal with three-dimensional (3D) non-Newtonian flows with complex free surfaces, in which the viscosity is modeled using the Cross model. In order to alleviate the so-called tensile instability which leads to particle clustering and unphysical fracture in fluid stretching, an artificial stress term is particularly incorporated into the momentum equation. For convenience in implementation of wall boundary condition in 3D, an enhanced treatment of solid boundaries is proposed to improve the computational performance. Parallelization is also developed to ensure affordable computational time of simulations involving millions of particles. The proposed SPH algorithm is validated by solving the Hagen–Poiseuille flow and comparing the SPH results with the available analytical solutions. To demonstrate the ability of the numerical method in simulating 3D non-Newtonian flows with free surfaces, three challenging engineering applications, including the impacting droplet, molding injection of a thin plate mold and a Z-shaped mold, and jet buckling, are investigated. It is found that the shear-thinning behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and fairly accurate and agrees well with the available data.