High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi = 85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considered including flow past a periodic array of cylinders and jet buckling. This work presents a significant step change in capabilities compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.