Smoothed particle hydrodynamics simulation of non-Newtonian moulding flow

Smoothed particle hydrodynamics (SPH) has been widely applied in simulating fluid flow because of its attractive properties, for example, it is fully Lagrangian and mesh free. However, this method usually uses the explicit method to solve the conservation equations and in this form it is only suitable to momentum dominated flows with low viscosity. In polymer processing, the fluid is non-Newtonian with high viscosity, O(10³) to O(10⁴) Pa-s say, and the pressure is high as O(10⁶) to O(10¹⁰) Pa. The algorithm of the standard SPH is infeasible in this case, because only very small time steps can be used for a stable simulation. We have developed an implicit SPH for non-Newtonian flow, which is completely matrix free, to solve the equation system iteratively and robustly. The artificial pressure is introduced between particles to stabilize the SPH system avoiding the tensile instability. The fluid is compressible under high pressure. Realistic state equations for polymers, such as the Tait and SSY 16] equations are adopted to describe the density/pressure relations. The method is finally applied to the simulation of moulding flow of a modified power law fluid with the zero shear rate viscosity of 1.22 × 10⁴ Pa-s, Reynolds number of 3 × 10^?4 to 6 × 10^?5 and the highest pressure of O(10⁸) to O(10¹⁰) Pa.